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sortie.txt
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################### METHODE DES DIFFERENCES FINIES ########################
***********************************************************************************************************************************************************
* ======================================================================================================================================================= *
* | f(x) = 1
* | u(x) = -0.5*x*x - 4.5*x +10
* | u(0) = [ 10.0 ]
* | u(1) = [ 5.0 ]
* ======================================================================================================================================================= *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | Point | Valeur Approchee | Valeur Exacte | Erreur | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | 0,100000 | 10,575385 | 9,545000 | 1,030385 | *
* | 0,110000 | 10,990769 | 9,498950 | 1,491819 | *
* | 0,120000 | 11,246154 | 9,452800 | 1,793354 | *
* | 0,130000 | 11,341538 | 9,406550 | 1,934988 | *
* | 0,150000 | 11,276923 | 9,313750 | 1,963173 | *
* | 0,160000 | 11,052308 | 9,267200 | 1,785108 | *
* | 0,170000 | 10,667692 | 9,220550 | 1,447142 | *
* | 0,200000 | 10,123077 | 9,080000 | 1,043077 | *
* | 0,470000 | 9,418462 | 7,774550 | 1,643912 | *
* | 0,480000 | 8,553846 | 7,724800 | 0,829046 | *
* | 0,500000 | 7,529231 | 7,625000 | 0,095769 | *
* | 0,900000 | 6,344615 | 5,545000 | 0,799615 | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* erreur infinie : 1.96317307692307
***********************************************************************************************************************************************************
i 0
i 1
i 2
***********************************************************************************************************************************************************
* ======================================================================================================================================================= *
* | f(x) = cos(x)
* | u(x) = cos(x)-(1+cos(1))*x-1
* | u(0) = [ 0.0 ]
* | u(1) = [ 0.0 ]
* ======================================================================================================================================================= *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | Point | Valeur Approchee | Valeur Exacte | Erreur | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | 0,008929 | 0,004065 | -0,013793 | 0,017857 | *
* | 0,017857 | 0,008050 | -0,027665 | 0,035714 | *
* | 0,026786 | 0,011955 | -0,041617 | 0,053572 | *
* | 0,035714 | 0,015780 | -0,055648 | 0,071429 | *
* | 0,044643 | 0,019526 | -0,069760 | 0,089286 | *
* | 0,053571 | 0,023192 | -0,083951 | 0,107143 | *
* | 0,062500 | 0,026779 | -0,098221 | 0,125000 | *
* | 0,071429 | 0,030286 | -0,112572 | 0,142857 | *
* | 0,080357 | 0,033713 | -0,127001 | 0,160715 | *
* | 0,089286 | 0,037061 | -0,141510 | 0,178572 | *
* | 0,098214 | 0,040330 | -0,156099 | 0,196429 | *
* | 0,107143 | 0,043519 | -0,170767 | 0,214286 | *
* | 0,116071 | 0,046629 | -0,185514 | 0,232143 | *
* | 0,125000 | 0,049660 | -0,200340 | 0,250000 | *
* | 0,133929 | 0,052612 | -0,215246 | 0,267857 | *
* | 0,142857 | 0,055485 | -0,230230 | 0,285715 | *
* | 0,151786 | 0,058279 | -0,245293 | 0,303572 | *
* | 0,160714 | 0,060994 | -0,260435 | 0,321429 | *
* | 0,169643 | 0,063630 | -0,275656 | 0,339286 | *
* | 0,178571 | 0,066188 | -0,290956 | 0,357143 | *
* | 0,187500 | 0,068667 | -0,306333 | 0,375000 | *
* | 0,196429 | 0,071068 | -0,321790 | 0,392858 | *
* | 0,205357 | 0,073391 | -0,337324 | 0,410715 | *
* | 0,214286 | 0,075636 | -0,352936 | 0,428572 | *
* | 0,223214 | 0,077803 | -0,368627 | 0,446429 | *
* | 0,232143 | 0,079892 | -0,384395 | 0,464286 | *
* | 0,241071 | 0,081903 | -0,400240 | 0,482143 | *
* | 0,250000 | 0,083837 | -0,416163 | 0,500001 | *
* | 0,258929 | 0,085694 | -0,432163 | 0,517858 | *
* | 0,267857 | 0,087474 | -0,448241 | 0,535715 | *
* | 0,276786 | 0,089177 | -0,464395 | 0,553572 | *
* | 0,285714 | 0,090803 | -0,480626 | 0,571429 | *
* | 0,294643 | 0,092353 | -0,496933 | 0,589286 | *
* | 0,303571 | 0,093827 | -0,513317 | 0,607143 | *
* | 0,312500 | 0,095224 | -0,529777 | 0,625001 | *
* | 0,321429 | 0,096546 | -0,546312 | 0,642858 | *
* | 0,330357 | 0,097792 | -0,562923 | 0,660715 | *
* | 0,339286 | 0,098962 | -0,579610 | 0,678572 | *
* | 0,348214 | 0,100058 | -0,596372 | 0,696429 | *
* | 0,357143 | 0,101078 | -0,613208 | 0,714286 | *
* | 0,366071 | 0,102024 | -0,630120 | 0,732144 | *
* | 0,375000 | 0,102895 | -0,647106 | 0,750001 | *
* | 0,383929 | 0,103692 | -0,664166 | 0,767858 | *
* | 0,392857 | 0,104415 | -0,681300 | 0,785715 | *
* | 0,401786 | 0,105065 | -0,698507 | 0,803572 | *
* | 0,410714 | 0,105641 | -0,715788 | 0,821429 | *
* | 0,419643 | 0,106144 | -0,733142 | 0,839286 | *
* | 0,428571 | 0,106574 | -0,750569 | 0,857144 | *
* | 0,437500 | 0,106932 | -0,768069 | 0,875001 | *
* | 0,446429 | 0,107218 | -0,785640 | 0,892858 | *
* | 0,455357 | 0,107431 | -0,803284 | 0,910715 | *
* | 0,464286 | 0,107573 | -0,820999 | 0,928572 | *
* | 0,473214 | 0,107644 | -0,838785 | 0,946429 | *
* | 0,482143 | 0,107644 | -0,856642 | 0,964286 | *
* | 0,491071 | 0,107573 | -0,874570 | 0,982144 | *
* | 0,500000 | 0,107432 | -0,892569 | 1,000001 | *
* | 0,508929 | 0,107221 | -0,910637 | 1,017858 | *
* | 0,517857 | 0,106940 | -0,928775 | 1,035715 | *
* | 0,526786 | 0,106590 | -0,946982 | 1,053572 | *
* | 0,535714 | 0,106172 | -0,965258 | 1,071429 | *
* | 0,544643 | 0,105684 | -0,983602 | 1,089286 | *
* | 0,553571 | 0,105129 | -1,002015 | 1,107144 | *
* | 0,562500 | 0,104505 | -1,020496 | 1,125001 | *
* | 0,571429 | 0,103814 | -1,039044 | 1,142858 | *
* | 0,580357 | 0,103056 | -1,057659 | 1,160715 | *
* | 0,589286 | 0,102232 | -1,076340 | 1,178572 | *
* | 0,598214 | 0,101341 | -1,095088 | 1,196429 | *
* | 0,607143 | 0,100384 | -1,113902 | 1,214286 | *
* | 0,616071 | 0,099362 | -1,132781 | 1,232144 | *
* | 0,625000 | 0,098275 | -1,151726 | 1,250001 | *
* | 0,633929 | 0,097123 | -1,170735 | 1,267858 | *
* | 0,642857 | 0,095907 | -1,189808 | 1,285715 | *
* | 0,651786 | 0,094627 | -1,208945 | 1,303572 | *
* | 0,660714 | 0,093284 | -1,228146 | 1,321429 | *
* | 0,669643 | 0,091877 | -1,247409 | 1,339286 | *
* | 0,678571 | 0,090409 | -1,266735 | 1,357143 | *
* | 0,687500 | 0,088878 | -1,286123 | 1,375001 | *
* | 0,696429 | 0,087285 | -1,305572 | 1,392858 | *
* | 0,705357 | 0,085632 | -1,325083 | 1,410715 | *
* | 0,714286 | 0,083917 | -1,344655 | 1,428572 | *
* | 0,723214 | 0,082143 | -1,364286 | 1,446429 | *
* | 0,732143 | 0,080309 | -1,383978 | 1,464286 | *
* | 0,741071 | 0,078415 | -1,403728 | 1,482143 | *
* | 0,750000 | 0,076463 | -1,423538 | 1,500001 | *
* | 0,758929 | 0,074452 | -1,443406 | 1,517858 | *
* | 0,767857 | 0,072383 | -1,463331 | 1,535715 | *
* | 0,776786 | 0,070257 | -1,483314 | 1,553572 | *
* | 0,785714 | 0,068075 | -1,503354 | 1,571429 | *
* | 0,794643 | 0,065836 | -1,523451 | 1,589286 | *
* | 0,803571 | 0,063541 | -1,543603 | 1,607143 | *
* | 0,812500 | 0,061190 | -1,563810 | 1,625000 | *
* | 0,821429 | 0,058785 | -1,584072 | 1,642858 | *
* | 0,830357 | 0,056326 | -1,604389 | 1,660715 | *
* | 0,839286 | 0,053813 | -1,624759 | 1,678572 | *
* | 0,848214 | 0,051246 | -1,645183 | 1,696429 | *
* | 0,857143 | 0,048627 | -1,665659 | 1,714286 | *
* | 0,866071 | 0,045956 | -1,686188 | 1,732143 | *
* | 0,875000 | 0,043233 | -1,706768 | 1,750000 | *
* | 0,883929 | 0,040459 | -1,727399 | 1,767857 | *
* | 0,892857 | 0,037634 | -1,748081 | 1,785715 | *
* | 0,901786 | 0,034759 | -1,768812 | 1,803572 | *
* | 0,910714 | 0,031835 | -1,789594 | 1,821429 | *
* | 0,919643 | 0,028862 | -1,810424 | 1,839286 | *
* | 0,928571 | 0,025841 | -1,831302 | 1,857143 | *
* | 0,937500 | 0,022772 | -1,852228 | 1,875000 | *
* | 0,946429 | 0,019656 | -1,873202 | 1,892857 | *
* | 0,955357 | 0,016493 | -1,894222 | 1,910714 | *
* | 0,964286 | 0,013284 | -1,915288 | 1,928572 | *
* | 0,973214 | 0,010030 | -1,936399 | 1,946429 | *
* | 0,982143 | 0,006730 | -1,957555 | 1,964286 | *
* | 0,991071 | 0,003387 | -1,978756 | 1,982143 | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* erreur infinie : 1.9821428796441036
***********************************************************************************************************************************************************
i 0
i 1
i 2
***********************************************************************************************************************************************************
* ======================================================================================================================================================= *
* | f(x) = 1
* | u(x) = -0.5*x*x - 9/2*x +10
* | u(0) = [ 10.0 ]
* | u(1) = [ 5.0 ]
* ======================================================================================================================================================= *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | Point | Valeur Approchee | Valeur Exacte | Erreur | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | 0,250000 | 8,933750 | 8,843750 | 0,090000 | *
* | 0,400000 | 7,745000 | 8,120000 | 0,375000 | *
* | 0,750000 | 6,433750 | 6,343750 | 0,090000 | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* erreur infinie : 0.3749999999999991
***********************************************************************************************************************************************************
i 0
i 1
i 2
***********************************************************************************************************************************************************
* ======================================================================================================================================================= *
* | f(x) = 1
* | u(x) = -0.5*x*x - 9/2*x +10
* | u(0) = [ 10.0 ]
* | u(1) = [ 5.0 ]
* ======================================================================================================================================================= *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | Point | Valeur Approchee | Valeur Exacte | Erreur | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | 0,250000 | 8,843750 | 8,843750 | 0,000000 | *
* | 0,500000 | 7,625000 | 7,625000 | 0,000000 | *
* | 0,750000 | 6,343750 | 6,343750 | 0,000000 | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* erreur infinie : 1.7763568394002505E-15
***********************************************************************************************************************************************************
i 0
i 1
i 2
***********************************************************************************************************************************************************
* ======================================================================================================================================================= *
* | f(x) = x
* | u(x) = -1/6 * x*x*x - 29/6 * x +10
* | u(0) = [ 10.0 ]
* | u(1) = [ 5.0 ]
* ======================================================================================================================================================= *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | Point | Valeur Approchee | Valeur Exacte | Erreur | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | 0,250000 | 8,820438 | 8,789063 | 0,031375 | *
* | 0,400000 | 7,610250 | 8,056000 | 0,445750 | *
* | 0,750000 | 6,351062 | 6,304688 | 0,046375 | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* erreur infinie : 0.4457500000000012
***********************************************************************************************************************************************************
i 0
i 1
i 2
***********************************************************************************************************************************************************
* ======================================================================================================================================================= *
* | f(x) = x
* | u(x) = -1/6 * x*x*x - 29/6 * x +10
* | u(0) = [ 10.0 ]
* | u(1) = [ 5.0 ]
* ======================================================================================================================================================= *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | Point | Valeur Approchee | Valeur Exacte | Erreur | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | 0,250000 | 8,789063 | 8,789063 | 0,000000 | *
* | 0,500000 | 7,562500 | 7,562500 | 0,000000 | *
* | 0,750000 | 6,304687 | 6,304688 | 0,000000 | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* erreur infinie : 8.881784197001252E-16
***********************************************************************************************************************************************************
i 0
i 1
i 2
***********************************************************************************************************************************************************
* ======================================================================================================================================================= *
* | f(x) = x
* | u(x) = -1/6 * x*x*x - 29/6 * x +10
* | u(0) = [ 10.0 ]
* | u(1) = [ 5.0 ]
* ======================================================================================================================================================= *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | Point | Valeur Approchee | Valeur Exacte | Erreur | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | 0,100000 | 9,516500 | 9,516500 | 0,000000 | *
* | 0,200000 | 9,032000 | 9,032000 | 0,000000 | *
* | 0,300000 | 8,545500 | 8,545500 | 0,000000 | *
* | 0,400000 | 8,056000 | 8,056000 | 0,000000 | *
* | 0,500000 | 7,562500 | 7,562500 | 0,000000 | *
* | 0,600000 | 7,064000 | 7,064000 | 0,000000 | *
* | 0,700000 | 6,559500 | 6,559500 | 0,000000 | *
* | 0,800000 | 6,048000 | 6,048000 | 0,000000 | *
* | 0,900000 | 5,528500 | 5,528500 | 0,000000 | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* erreur infinie : 2.6645352591003757E-15
***********************************************************************************************************************************************************
i 0
i 1
i 2
***********************************************************************************************************************************************************
* ======================================================================================================================================================= *
* | f(x) = 1.0/x
* | u(x) = -x*log(x) + x + 1
* | u(0) = [ 1.0 ]
* | u(1) = [ 2.0 ]
* ======================================================================================================================================================= *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | Point | Valeur Approchee | Valeur Exacte | Erreur | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | 0,250000 | 1,520833 | 1,596574 | 0,075740 | *
* | 0,500000 | 1,791667 | 1,846574 | 0,054907 | *
* | 0,750000 | 1,937500 | 1,965762 | 0,028262 | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* erreur infinie : 0.07574025694663922
***********************************************************************************************************************************************************
i 0
i 1
i 2
***********************************************************************************************************************************************************
* ======================================================================================================================================================= *
* | f(x) = 1.0/x
* | u(x) = -x*log(x) + x + 1
* | u(0) = [ 1.0 ]
* | u(1) = [ 2.0 ]
* ======================================================================================================================================================= *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | Point | Valeur Approchee | Valeur Exacte | Erreur | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | 0,032258 | 1,129911 | 1,143032 | 0,013121 | *
* | 0,064516 | 1,227564 | 1,241345 | 0,013780 | *
* | 0,096774 | 1,309088 | 1,322778 | 0,013690 | *
* | 0,129032 | 1,379860 | 1,393251 | 0,013391 | *
* | 0,161290 | 1,442566 | 1,455572 | 0,013006 | *
* | 0,193548 | 1,498822 | 1,511399 | 0,012577 | *
* | 0,225806 | 1,549701 | 1,561824 | 0,012123 | *
* | 0,258065 | 1,595971 | 1,607625 | 0,011654 | *
* | 0,290323 | 1,638209 | 1,649383 | 0,011173 | *
* | 0,322581 | 1,676864 | 1,687549 | 0,010686 | *
* | 0,354839 | 1,712292 | 1,722484 | 0,010192 | *
* | 0,387097 | 1,744788 | 1,754483 | 0,009695 | *
* | 0,419355 | 1,774595 | 1,783790 | 0,009195 | *
* | 0,451613 | 1,801921 | 1,810613 | 0,008692 | *
* | 0,483871 | 1,826943 | 1,835131 | 0,008187 | *
* | 0,516129 | 1,849815 | 1,857496 | 0,007681 | *
* | 0,548387 | 1,870670 | 1,877844 | 0,007174 | *
* | 0,580645 | 1,889628 | 1,896293 | 0,006665 | *
* | 0,612903 | 1,906794 | 1,912949 | 0,006155 | *
* | 0,645161 | 1,922262 | 1,927906 | 0,005645 | *
* | 0,677419 | 1,936117 | 1,941250 | 0,005134 | *
* | 0,709677 | 1,948436 | 1,953058 | 0,004622 | *
* | 0,741935 | 1,959288 | 1,963398 | 0,004110 | *
* | 0,774194 | 1,968738 | 1,972336 | 0,003597 | *
* | 0,806452 | 1,976844 | 1,979929 | 0,003084 | *
* | 0,838710 | 1,983660 | 1,986231 | 0,002571 | *
* | 0,870968 | 1,989235 | 1,991292 | 0,002057 | *
* | 0,903226 | 1,993615 | 1,995159 | 0,001543 | *
* | 0,935484 | 1,996844 | 1,997873 | 0,001029 | *
* | 0,967742 | 1,998959 | 1,999474 | 0,000515 | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* erreur infinie : 0.013780311515398713
***********************************************************************************************************************************************************
i 0
i 1
i 2
***********************************************************************************************************************************************************
* ======================================================================================================================================================= *
* | f(x) = 1.0/x
* | u(x) = -x*log(x) + x + 1
* | u(0) = [ 1.0 ]
* | u(1) = [ 2.0 ]
* ======================================================================================================================================================= *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | Point | Valeur Approchee | Valeur Exacte | Erreur | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | 0,019608 | 1,088604 | 1,096702 | 0,008098 | *
* | 0,039216 | 1,157601 | 1,166223 | 0,008622 | *
* | 0,058824 | 1,216793 | 1,225483 | 0,008690 | *
* | 0,078431 | 1,269449 | 1,278081 | 0,008631 | *
* | 0,098039 | 1,317204 | 1,325724 | 0,008520 | *
* | 0,117647 | 1,361037 | 1,369420 | 0,008383 | *
* | 0,137255 | 1,401602 | 1,409832 | 0,008230 | *
* | 0,156863 | 1,439366 | 1,447433 | 0,008067 | *
* | 0,176471 | 1,474679 | 1,482577 | 0,007898 | *
* | 0,196078 | 1,507813 | 1,515537 | 0,007725 | *
* | 0,215686 | 1,538986 | 1,546534 | 0,007548 | *
* | 0,235294 | 1,568377 | 1,575746 | 0,007369 | *
* | 0,254902 | 1,596134 | 1,603321 | 0,007187 | *
* | 0,274510 | 1,622383 | 1,629387 | 0,007005 | *
* | 0,294118 | 1,647231 | 1,654052 | 0,006821 | *
* | 0,313725 | 1,670772 | 1,677408 | 0,006636 | *
* | 0,333333 | 1,693087 | 1,699537 | 0,006451 | *
* | 0,352941 | 1,714249 | 1,720513 | 0,006264 | *
* | 0,372549 | 1,734322 | 1,740399 | 0,006077 | *
* | 0,392157 | 1,753362 | 1,759252 | 0,005890 | *
* | 0,411765 | 1,771422 | 1,777125 | 0,005702 | *
* | 0,431373 | 1,788549 | 1,794063 | 0,005514 | *
* | 0,450980 | 1,804784 | 1,810110 | 0,005326 | *
* | 0,470588 | 1,820167 | 1,825304 | 0,005137 | *
* | 0,490196 | 1,834733 | 1,839681 | 0,004948 | *
* | 0,509804 | 1,848514 | 1,853274 | 0,004759 | *
* | 0,529412 | 1,861542 | 1,866112 | 0,004570 | *
* | 0,549020 | 1,873843 | 1,878223 | 0,004381 | *
* | 0,568627 | 1,885444 | 1,889635 | 0,004191 | *
* | 0,588235 | 1,896368 | 1,900370 | 0,004001 | *
* | 0,607843 | 1,906639 | 1,910451 | 0,003811 | *
* | 0,627451 | 1,916278 | 1,919899 | 0,003621 | *
* | 0,647059 | 1,925304 | 1,928735 | 0,003431 | *
* | 0,666667 | 1,933735 | 1,936977 | 0,003241 | *
* | 0,686275 | 1,941590 | 1,944641 | 0,003051 | *
* | 0,705882 | 1,948885 | 1,951746 | 0,002861 | *
* | 0,725490 | 1,955635 | 1,958306 | 0,002670 | *
* | 0,745098 | 1,961855 | 1,964335 | 0,002480 | *
* | 0,764706 | 1,967560 | 1,969849 | 0,002289 | *
* | 0,784314 | 1,972761 | 1,974860 | 0,002099 | *
* | 0,803922 | 1,977472 | 1,979380 | 0,001908 | *
* | 0,823529 | 1,981705 | 1,983423 | 0,001718 | *
* | 0,843137 | 1,985471 | 1,986998 | 0,001527 | *
* | 0,862745 | 1,988781 | 1,990117 | 0,001336 | *
* | 0,882353 | 1,991646 | 1,992791 | 0,001145 | *
* | 0,901961 | 1,994074 | 1,995029 | 0,000955 | *
* | 0,921569 | 1,996077 | 1,996841 | 0,000764 | *
* | 0,941176 | 1,997662 | 1,998235 | 0,000573 | *
* | 0,960784 | 1,998839 | 1,999221 | 0,000382 | *
* | 0,980392 | 1,999616 | 1,999806 | 0,000191 | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* erreur infinie : 0.00869020564252021
***********************************************************************************************************************************************************
i 0
i 1
i 2
***********************************************************************************************************************************************************
* ======================================================================================================================================================= *
* | f(x) = 1.0/x
* | u(x) = -x*log(x) + x + 1
* | u(0) = [ 1.0 ]
* | u(1) = [ 2.0 ]
* ======================================================================================================================================================= *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | Point | Valeur Approchee | Valeur Exacte | Erreur | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | 0,009901 | 1,051458 | 1,055595 | 0,004137 | *
* | 0,019802 | 1,093015 | 1,097465 | 0,004449 | *
* | 0,029703 | 1,129622 | 1,134154 | 0,004532 | *
* | 0,039604 | 1,162929 | 1,167478 | 0,004550 | *
* | 0,049505 | 1,193760 | 1,198301 | 0,004541 | *
* | 0,059406 | 1,222611 | 1,227130 | 0,004520 | *
* | 0,069307 | 1,249811 | 1,254302 | 0,004490 | *
* | 0,079208 | 1,275598 | 1,280054 | 0,004456 | *
* | 0,089109 | 1,300146 | 1,304565 | 0,004419 | *
* | 0,099010 | 1,323595 | 1,327974 | 0,004379 | *
* | 0,108911 | 1,346054 | 1,350391 | 0,004337 | *
* | 0,118812 | 1,367612 | 1,371907 | 0,004295 | *
* | 0,128713 | 1,388345 | 1,392596 | 0,004251 | *
* | 0,138614 | 1,408317 | 1,412524 | 0,004207 | *
* | 0,148515 | 1,427582 | 1,431743 | 0,004162 | *
* | 0,158416 | 1,446186 | 1,450302 | 0,004116 | *
* | 0,168317 | 1,464172 | 1,468242 | 0,004070 | *
* | 0,178218 | 1,481575 | 1,485599 | 0,004024 | *
* | 0,188119 | 1,498428 | 1,502405 | 0,003977 | *
* | 0,198020 | 1,514760 | 1,518691 | 0,003931 | *
* | 0,207921 | 1,530597 | 1,534481 | 0,003884 | *
* | 0,217822 | 1,545963 | 1,549799 | 0,003836 | *
* | 0,227723 | 1,560878 | 1,564667 | 0,003789 | *
* | 0,237624 | 1,575363 | 1,579105 | 0,003742 | *
* | 0,247525 | 1,589436 | 1,593130 | 0,003694 | *
* | 0,257426 | 1,603112 | 1,606759 | 0,003646 | *
* | 0,267327 | 1,616408 | 1,620007 | 0,003599 | *
* | 0,277228 | 1,629337 | 1,632888 | 0,003551 | *
* | 0,287129 | 1,641912 | 1,645415 | 0,003503 | *
* | 0,297030 | 1,654146 | 1,657601 | 0,003455 | *
* | 0,306931 | 1,666050 | 1,669457 | 0,003407 | *
* | 0,316832 | 1,677634 | 1,680993 | 0,003359 | *
* | 0,326733 | 1,688909 | 1,692220 | 0,003311 | *
* | 0,336634 | 1,699884 | 1,703147 | 0,003262 | *
* | 0,346535 | 1,710568 | 1,713783 | 0,003214 | *
* | 0,356436 | 1,720969 | 1,724135 | 0,003166 | *
* | 0,366337 | 1,731095 | 1,734213 | 0,003118 | *
* | 0,376238 | 1,740954 | 1,744023 | 0,003069 | *
* | 0,386139 | 1,750551 | 1,753572 | 0,003021 | *
* | 0,396040 | 1,759895 | 1,762868 | 0,002973 | *
* | 0,405941 | 1,768992 | 1,771916 | 0,002924 | *
* | 0,415842 | 1,777847 | 1,780722 | 0,002876 | *
* | 0,425743 | 1,786466 | 1,789293 | 0,002827 | *
* | 0,435644 | 1,794855 | 1,797633 | 0,002779 | *
* | 0,445545 | 1,803018 | 1,805749 | 0,002730 | *
* | 0,455446 | 1,810962 | 1,813644 | 0,002682 | *
* | 0,465347 | 1,818691 | 1,821324 | 0,002633 | *
* | 0,475248 | 1,826209 | 1,828793 | 0,002584 | *
* | 0,485149 | 1,833521 | 1,836057 | 0,002536 | *
* | 0,495050 | 1,840630 | 1,843118 | 0,002487 | *
* | 0,504950 | 1,847542 | 1,849981 | 0,002439 | *
* | 0,514851 | 1,854259 | 1,856649 | 0,002390 | *
* | 0,524752 | 1,860786 | 1,863128 | 0,002341 | *
* | 0,534653 | 1,867127 | 1,869419 | 0,002293 | *
* | 0,544554 | 1,873284 | 1,875528 | 0,002244 | *
* | 0,554455 | 1,879261 | 1,881456 | 0,002195 | *
* | 0,564356 | 1,885061 | 1,887207 | 0,002147 | *
* | 0,574257 | 1,890687 | 1,892785 | 0,002098 | *
* | 0,584158 | 1,896143 | 1,898192 | 0,002049 | *
* | 0,594059 | 1,901431 | 1,903431 | 0,002001 | *
* | 0,603960 | 1,906553 | 1,908505 | 0,001952 | *
* | 0,613861 | 1,911514 | 1,913417 | 0,001903 | *
* | 0,623762 | 1,916315 | 1,918169 | 0,001855 | *
* | 0,633663 | 1,920958 | 1,922764 | 0,001806 | *
* | 0,643564 | 1,925447 | 1,927205 | 0,001757 | *
* | 0,653465 | 1,929784 | 1,931492 | 0,001708 | *
* | 0,663366 | 1,933971 | 1,935630 | 0,001660 | *
* | 0,673267 | 1,938010 | 1,939621 | 0,001611 | *
* | 0,683168 | 1,941903 | 1,943465 | 0,001562 | *
* | 0,693069 | 1,945653 | 1,947166 | 0,001513 | *
* | 0,702970 | 1,949261 | 1,950726 | 0,001465 | *
* | 0,712871 | 1,952730 | 1,954146 | 0,001416 | *
* | 0,722772 | 1,956061 | 1,957428 | 0,001367 | *
* | 0,732673 | 1,959257 | 1,960575 | 0,001318 | *
* | 0,742574 | 1,962319 | 1,963588 | 0,001269 | *
* | 0,752475 | 1,965249 | 1,966470 | 0,001221 | *
* | 0,762376 | 1,968049 | 1,969220 | 0,001172 | *
* | 0,772277 | 1,970720 | 1,971843 | 0,001123 | *
* | 0,782178 | 1,973264 | 1,974338 | 0,001074 | *
* | 0,792079 | 1,975683 | 1,976708 | 0,001025 | *
* | 0,801980 | 1,977978 | 1,978954 | 0,000977 | *
* | 0,811881 | 1,980150 | 1,981078 | 0,000928 | *
* | 0,821782 | 1,982202 | 1,983082 | 0,000879 | *
* | 0,831683 | 1,984135 | 1,984965 | 0,000830 | *
* | 0,841584 | 1,985950 | 1,986732 | 0,000781 | *
* | 0,851485 | 1,987649 | 1,988381 | 0,000733 | *
* | 0,861386 | 1,989232 | 1,989916 | 0,000684 | *
* | 0,871287 | 1,990701 | 1,991336 | 0,000635 | *
* | 0,881188 | 1,992058 | 1,992644 | 0,000586 | *
* | 0,891089 | 1,993304 | 1,993841 | 0,000537 | *
* | 0,900990 | 1,994440 | 1,994928 | 0,000488 | *
* | 0,910891 | 1,995467 | 1,995906 | 0,000440 | *
* | 0,920792 | 1,996386 | 1,996777 | 0,000391 | *
* | 0,930693 | 1,997199 | 1,997541 | 0,000342 | *
* | 0,940594 | 1,997906 | 1,998199 | 0,000293 | *
* | 0,950495 | 1,998510 | 1,998754 | 0,000244 | *
* | 0,960396 | 1,999010 | 1,999205 | 0,000195 | *
* | 0,970297 | 1,999408 | 1,999554 | 0,000147 | *
* | 0,980198 | 1,999705 | 1,999803 | 0,000098 | *
* | 0,990099 | 1,999902 | 1,999951 | 0,000049 | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* erreur infinie : 0.004549741834300791
***********************************************************************************************************************************************************
i 0
i 1
i 2
***********************************************************************************************************************************************************
* ======================================================================================================================================================= *
* | f(x) = x*x
* | u(x) = -1.0/12*x*x*x*x + ( 1.0/12 - 5)*x +10
* | u(0) = [ 10.0 ]
* | u(1) = [ 5.0 ]
* ======================================================================================================================================================= *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | Point | Valeur Approchee | Valeur Exacte | Erreur | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | 0,250000 | 8,769531 | 8,770508 | 0,000977 | *
* | 0,500000 | 7,535156 | 7,536458 | 0,001302 | *
* | 0,750000 | 6,285156 | 6,286133 | 0,000977 | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* erreur infinie : 0.0013020833333339255
***********************************************************************************************************************************************************
i 0
i 1
i 2
***********************************************************************************************************************************************************
* ======================================================================================================================================================= *
* | f(x) = x*x
* | u(x) = -1.0/12*x*x*x*x + ( 1.0/12 - 5)*x +10
* | u(0) = [ 10.0 ]
* | u(1) = [ 5.0 ]
* ======================================================================================================================================================= *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | Point | Valeur Approchee | Valeur Exacte | Erreur | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | 0,032258 | 9,841395 | 9,841398 | 0,000003 | *
* | 0,064516 | 9,682789 | 9,682794 | 0,000005 | *
* | 0,096774 | 9,524179 | 9,524186 | 0,000008 | *
* | 0,129032 | 9,365559 | 9,365568 | 0,000010 | *
* | 0,161290 | 9,206921 | 9,206933 | 0,000012 | *
* | 0,193548 | 9,048257 | 9,048270 | 0,000014 | *
* | 0,225806 | 8,889553 | 8,889568 | 0,000015 | *
* | 0,258065 | 8,730797 | 8,730813 | 0,000017 | *
* | 0,290323 | 8,571971 | 8,571989 | 0,000018 | *
* | 0,322581 | 8,413057 | 8,413076 | 0,000019 | *
* | 0,354839 | 8,254035 | 8,254055 | 0,000020 | *
* | 0,387097 | 8,094883 | 8,094903 | 0,000021 | *
* | 0,419355 | 7,935574 | 7,935595 | 0,000021 | *
* | 0,451613 | 7,776082 | 7,776103 | 0,000021 | *
* | 0,483871 | 7,616378 | 7,616400 | 0,000022 | *
* | 0,516129 | 7,456430 | 7,456452 | 0,000022 | *
* | 0,548387 | 7,296206 | 7,296227 | 0,000021 | *
* | 0,580645 | 7,135668 | 7,135689 | 0,000021 | *
* | 0,612903 | 6,974779 | 6,974800 | 0,000021 | *
* | 0,645161 | 6,813500 | 6,813519 | 0,000020 | *
* | 0,677419 | 6,651787 | 6,651806 | 0,000019 | *
* | 0,709677 | 6,489597 | 6,489615 | 0,000018 | *
* | 0,741935 | 6,326883 | 6,326899 | 0,000017 | *
* | 0,774194 | 6,163596 | 6,163611 | 0,000015 | *
* | 0,806452 | 5,999685 | 5,999698 | 0,000014 | *
* | 0,838710 | 5,835097 | 5,835109 | 0,000012 | *
* | 0,870968 | 5,669778 | 5,669788 | 0,000010 | *
* | 0,903226 | 5,503669 | 5,503677 | 0,000008 | *
* | 0,935484 | 5,336711 | 5,336717 | 0,000005 | *
* | 0,967742 | 5,168843 | 5,168846 | 0,000003 | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* erreur infinie : 2.1656248221368912E-5
***********************************************************************************************************************************************************
i 0
i 1
i 2
***********************************************************************************************************************************************************
* ======================================================================================================================================================= *
* | f(x) = x*x
* | u(x) = -1.0/12*x*x*x*x + ( 1.0/12 - 5)*x +10
* | u(0) = [ 10.0 ]
* | u(1) = [ 5.0 ]
* ======================================================================================================================================================= *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | Point | Valeur Approchee | Valeur Exacte | Erreur | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | 0,019608 | 9,903594 | 9,903595 | 0,000001 | *
* | 0,039216 | 9,807188 | 9,807189 | 0,000001 | *
* | 0,058824 | 9,710782 | 9,710783 | 0,000002 | *
* | 0,078431 | 9,614374 | 9,614376 | 0,000002 | *
* | 0,098039 | 9,517963 | 9,517966 | 0,000003 | *
* | 0,117647 | 9,421549 | 9,421553 | 0,000003 | *
* | 0,137255 | 9,325130 | 9,325134 | 0,000004 | *
* | 0,156863 | 9,228703 | 9,228708 | 0,000004 | *
* | 0,176471 | 9,132267 | 9,132272 | 0,000005 | *
* | 0,196078 | 9,035819 | 9,035825 | 0,000005 | *
* | 0,215686 | 8,939357 | 8,939362 | 0,000005 | *
* | 0,235294 | 8,842876 | 8,842882 | 0,000006 | *
* | 0,254902 | 8,746374 | 8,746380 | 0,000006 | *
* | 0,274510 | 8,649847 | 8,649854 | 0,000006 | *
* | 0,294118 | 8,553291 | 8,553298 | 0,000007 | *
* | 0,313725 | 8,456702 | 8,456709 | 0,000007 | *
* | 0,333333 | 8,360075 | 8,360082 | 0,000007 | *
* | 0,352941 | 8,263405 | 8,263413 | 0,000007 | *
* | 0,372549 | 8,166688 | 8,166695 | 0,000007 | *
* | 0,392157 | 8,069917 | 8,069925 | 0,000008 | *
* | 0,411765 | 7,973087 | 7,973095 | 0,000008 | *
* | 0,431373 | 7,876192 | 7,876199 | 0,000008 | *
* | 0,450980 | 7,779225 | 7,779233 | 0,000008 | *
* | 0,470588 | 7,682180 | 7,682188 | 0,000008 | *
* | 0,490196 | 7,585050 | 7,585058 | 0,000008 | *
* | 0,509804 | 7,487827 | 7,487835 | 0,000008 | *
* | 0,529412 | 7,390505 | 7,390513 | 0,000008 | *
* | 0,549020 | 7,293074 | 7,293082 | 0,000008 | *
* | 0,568627 | 7,195528 | 7,195536 | 0,000008 | *
* | 0,588235 | 7,097858 | 7,097866 | 0,000008 | *
* | 0,607843 | 7,000054 | 7,000062 | 0,000008 | *
* | 0,627451 | 6,902109 | 6,902116 | 0,000007 | *
* | 0,647059 | 6,804012 | 6,804019 | 0,000007 | *
* | 0,666667 | 6,705754 | 6,705761 | 0,000007 | *
* | 0,686275 | 6,607325 | 6,607332 | 0,000007 | *
* | 0,705882 | 6,508716 | 6,508722 | 0,000007 | *
* | 0,725490 | 6,409914 | 6,409921 | 0,000006 | *
* | 0,745098 | 6,310911 | 6,310917 | 0,000006 | *
* | 0,764706 | 6,211693 | 6,211699 | 0,000006 | *
* | 0,784314 | 6,112252 | 6,112257 | 0,000005 | *
* | 0,803922 | 6,012573 | 6,012578 | 0,000005 | *
* | 0,823529 | 5,912646 | 5,912651 | 0,000005 | *
* | 0,843137 | 5,812458 | 5,812463 | 0,000004 | *
* | 0,862745 | 5,711997 | 5,712001 | 0,000004 | *
* | 0,882353 | 5,611250 | 5,611253 | 0,000003 | *
* | 0,901961 | 5,510204 | 5,510206 | 0,000003 | *
* | 0,921569 | 5,408844 | 5,408847 | 0,000002 | *
* | 0,941176 | 5,307159 | 5,307160 | 0,000002 | *
* | 0,960784 | 5,205132 | 5,205133 | 0,000001 | *
* | 0,980392 | 5,102751 | 5,102751 | 0,000001 | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* erreur infinie : 8.006660328518933E-6
***********************************************************************************************************************************************************
i 0
i 1
i 2
***********************************************************************************************************************************************************
* ======================================================================================================================================================= *
* | f(x) = x*x
* | u(x) = -1.0/12*x*x*x*x + ( 1.0/12 - 5)*x +10
* | u(0) = [ 10.0 ]
* | u(1) = [ 5.0 ]
* ======================================================================================================================================================= *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | Point | Valeur Approchee | Valeur Exacte | Erreur | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | 0,009901 | 9,951320 | 9,951320 | 0,000000 | *
* | 0,019802 | 9,902640 | 9,902640 | 0,000000 | *
* | 0,029703 | 9,853960 | 9,853960 | 0,000000 | *
* | 0,039604 | 9,805280 | 9,805280 | 0,000000 | *
* | 0,049505 | 9,756600 | 9,756600 | 0,000000 | *
* | 0,059406 | 9,707919 | 9,707920 | 0,000000 | *
* | 0,069307 | 9,659238 | 9,659239 | 0,000001 | *
* | 0,079208 | 9,610557 | 9,610558 | 0,000001 | *
* | 0,089109 | 9,561875 | 9,561876 | 0,000001 | *
* | 0,099010 | 9,513193 | 9,513193 | 0,000001 | *
* | 0,108911 | 9,464509 | 9,464510 | 0,000001 | *
* | 0,118812 | 9,415824 | 9,415825 | 0,000001 | *
* | 0,128713 | 9,367138 | 9,367139 | 0,000001 | *
* | 0,138614 | 9,318450 | 9,318451 | 0,000001 | *
* | 0,148515 | 9,269760 | 9,269761 | 0,000001 | *
* | 0,158416 | 9,221069 | 9,221070 | 0,000001 | *
* | 0,168317 | 9,172374 | 9,172375 | 0,000001 | *
* | 0,178218 | 9,123677 | 9,123678 | 0,000001 | *
* | 0,188119 | 9,074977 | 9,074978 | 0,000001 | *
* | 0,198020 | 9,026273 | 9,026275 | 0,000001 | *
* | 0,207921 | 8,977566 | 8,977567 | 0,000001 | *
* | 0,217822 | 8,928854 | 8,928855 | 0,000001 | *
* | 0,227723 | 8,880137 | 8,880139 | 0,000001 | *
* | 0,237624 | 8,831416 | 8,831417 | 0,000001 | *
* | 0,247525 | 8,782689 | 8,782690 | 0,000002 | *
* | 0,257426 | 8,733956 | 8,733957 | 0,000002 | *
* | 0,267327 | 8,685216 | 8,685218 | 0,000002 | *
* | 0,277228 | 8,636470 | 8,636471 | 0,000002 | *
* | 0,287129 | 8,587716 | 8,587717 | 0,000002 | *
* | 0,297030 | 8,538954 | 8,538955 | 0,000002 | *
* | 0,306931 | 8,490183 | 8,490185 | 0,000002 | *
* | 0,316832 | 8,441403 | 8,441405 | 0,000002 | *
* | 0,326733 | 8,392613 | 8,392615 | 0,000002 | *
* | 0,336634 | 8,343813 | 8,343814 | 0,000002 | *
* | 0,346535 | 8,295001 | 8,295003 | 0,000002 | *
* | 0,356436 | 8,246178 | 8,246180 | 0,000002 | *
* | 0,366337 | 8,197342 | 8,197344 | 0,000002 | *
* | 0,376238 | 8,148493 | 8,148495 | 0,000002 | *
* | 0,386139 | 8,099631 | 8,099633 | 0,000002 | *
* | 0,396040 | 8,050753 | 8,050755 | 0,000002 | *
* | 0,405941 | 8,001861 | 8,001862 | 0,000002 | *
* | 0,415842 | 7,952952 | 7,952954 | 0,000002 | *
* | 0,425743 | 7,904026 | 7,904028 | 0,000002 | *
* | 0,435644 | 7,855082 | 7,855084 | 0,000002 | *
* | 0,445545 | 7,806120 | 7,806122 | 0,000002 | *
* | 0,455446 | 7,757138 | 7,757140 | 0,000002 | *
* | 0,465347 | 7,708136 | 7,708138 | 0,000002 | *
* | 0,475248 | 7,659113 | 7,659115 | 0,000002 | *
* | 0,485149 | 7,610068 | 7,610070 | 0,000002 | *
* | 0,495050 | 7,560999 | 7,561001 | 0,000002 | *
* | 0,504950 | 7,511907 | 7,511909 | 0,000002 | *
* | 0,514851 | 7,462790 | 7,462792 | 0,000002 | *
* | 0,524752 | 7,413646 | 7,413648 | 0,000002 | *
* | 0,534653 | 7,364476 | 7,364478 | 0,000002 | *
* | 0,544554 | 7,315277 | 7,315279 | 0,000002 | *
* | 0,554455 | 7,266050 | 7,266052 | 0,000002 | *
* | 0,564356 | 7,216792 | 7,216794 | 0,000002 | *
* | 0,574257 | 7,167503 | 7,167505 | 0,000002 | *
* | 0,584158 | 7,118182 | 7,118184 | 0,000002 | *
* | 0,594059 | 7,068827 | 7,068829 | 0,000002 | *
* | 0,603960 | 7,019438 | 7,019440 | 0,000002 | *
* | 0,613861 | 6,970013 | 6,970015 | 0,000002 | *
* | 0,623762 | 6,920551 | 6,920553 | 0,000002 | *
* | 0,633663 | 6,871051 | 6,871053 | 0,000002 | *
* | 0,643564 | 6,821512 | 6,821513 | 0,000002 | *
* | 0,653465 | 6,771932 | 6,771933 | 0,000002 | *
* | 0,663366 | 6,722310 | 6,722311 | 0,000002 | *
* | 0,673267 | 6,672645 | 6,672646 | 0,000002 | *
* | 0,683168 | 6,622935 | 6,622937 | 0,000002 | *
* | 0,693069 | 6,573180 | 6,573182 | 0,000002 | *
* | 0,702970 | 6,523378 | 6,523379 | 0,000002 | *
* | 0,712871 | 6,473527 | 6,473528 | 0,000002 | *
* | 0,722772 | 6,423626 | 6,423628 | 0,000002 | *
* | 0,732673 | 6,373674 | 6,373676 | 0,000002 | *
* | 0,742574 | 6,323670 | 6,323672 | 0,000002 | *
* | 0,752475 | 6,273612 | 6,273613 | 0,000002 | *
* | 0,762376 | 6,223498 | 6,223499 | 0,000001 | *
* | 0,772277 | 6,173327 | 6,173328 | 0,000001 | *
* | 0,782178 | 6,123097 | 6,123099 | 0,000001 | *
* | 0,792079 | 6,072808 | 6,072809 | 0,000001 | *
* | 0,801980 | 6,022457 | 6,022458 | 0,000001 | *
* | 0,811881 | 5,972043 | 5,972044 | 0,000001 | *
* | 0,821782 | 5,921564 | 5,921566 | 0,000001 | *
* | 0,831683 | 5,871020 | 5,871021 | 0,000001 | *
* | 0,841584 | 5,820407 | 5,820408 | 0,000001 | *
* | 0,851485 | 5,769725 | 5,769726 | 0,000001 | *
* | 0,861386 | 5,718972 | 5,718973 | 0,000001 | *
* | 0,871287 | 5,668146 | 5,668147 | 0,000001 | *
* | 0,881188 | 5,617246 | 5,617247 | 0,000001 | *
* | 0,891089 | 5,566269 | 5,566270 | 0,000001 | *
* | 0,900990 | 5,515215 | 5,515216 | 0,000001 | *
* | 0,910891 | 5,464082 | 5,464082 | 0,000001 | *
* | 0,920792 | 5,412866 | 5,412867 | 0,000001 | *
* | 0,930693 | 5,361568 | 5,361569 | 0,000001 | *
* | 0,940594 | 5,310185 | 5,310185 | 0,000000 | *
* | 0,950495 | 5,258715 | 5,258716 | 0,000000 | *
* | 0,960396 | 5,207157 | 5,207157 | 0,000000 | *
* | 0,970297 | 5,155508 | 5,155508 | 0,000000 | *
* | 0,980198 | 5,103767 | 5,103767 | 0,000000 | *
* | 0,990099 | 5,051931 | 5,051932 | 0,000000 | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* erreur infinie : 2.0420832607115358E-6
***********************************************************************************************************************************************************
i 0
i 1
i 2
***********************************************************************************************************************************************************
* ======================================================================================================================================================= *
* | f(x) = sqrt(x)
* | u(x) = (-4.0/15) * x * ( x * sqrt(x) +1)
* | u(0) = [ 0.0 ]
* | u(1) = [ 0.0 ]
* ======================================================================================================================================================= *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | Point | Valeur Approchee | Valeur Exacte | Erreur | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | 0,250000 | 0,059066 | -0,075000 | 0,134066 | *
* | 0,500000 | 0,086882 | -0,180474 | 0,267356 | *
* | 0,750000 | 0,070505 | -0,329904 | 0,400408 | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* erreur infinie : 0.40040833828214095
***********************************************************************************************************************************************************
i 0
i 1
i 2
***********************************************************************************************************************************************************
* ======================================================================================================================================================= *
* | f(x) = sqrt(x)
* | u(x) = (-4.0/15) * x * ( x * sqrt(x) +1)
* | u(0) = [ 0.0 ]
* | u(1) = [ 0.0 ]
* ======================================================================================================================================================= *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | Point | Valeur Approchee | Valeur Exacte | Erreur | *
* ------------------------------------------------------------------------------------------------------------------------------------------------------- *
* | 0,032258 | 0,008561 | -0,008652 | 0,017213 | *
* | 0,064516 | 0,016934 | -0,017486 | 0,034421 | *
* | 0,096774 | 0,025044 | -0,026583 | 0,051627 | *
* | 0,129032 | 0,032830 | -0,036003 | 0,068833 | *
* | 0,161290 | 0,040242 | -0,045797 | 0,086038 | *
* | 0,193548 | 0,047236 | -0,056008 | 0,103243 | *