-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathnumerical-analysis.nb
6161 lines (6121 loc) · 344 KB
/
numerical-analysis.nb
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 10.2' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 158, 7]
NotebookDataLength[ 352167, 6152]
NotebookOptionsPosition[ 350542, 6099]
NotebookOutlinePosition[ 350882, 6114]
CellTagsIndexPosition[ 350839, 6111]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{"RK", "[",
RowBox[{"f_", ",", "t_", ",", "x_", ",", "h_", ",", "n_"}], "]"}], ":=",
RowBox[{"(*",
RowBox[{"adding", " ",
RowBox[{"N", "[",
RowBox[{",", "30"}], "]"}], " ", "makes", " ", "our", " ",
"calculation", " ", "more", " ",
RowBox[{"precise", ".", "But"}], " ", "we", " ", "need", " ", "to", " ",
"take", " ", "out", " ", "1.", " ", "in", " ", "places"}], "*)"}],
RowBox[{"Module", "[",
RowBox[{
RowBox[{"{",
RowBox[{"i", ",",
RowBox[{"s", "=", "t"}], ",", "k1", ",", "k2", ",", "k3", ",", "k4",
",",
RowBox[{"y", "=", "x"}], ",",
RowBox[{"h2", "=",
RowBox[{"N", "[",
RowBox[{
RowBox[{"h", "/", "2"}], ",", "30"}], "]"}]}]}], "}"}], ",",
RowBox[{
RowBox[{"For", "[",
RowBox[{
RowBox[{"i", "=", "1"}], ",",
RowBox[{"i", "\[LessEqual]", "n"}], ",",
RowBox[{"i", "++"}], ",",
RowBox[{
RowBox[{"k1", "=",
RowBox[{"h", "*",
RowBox[{"f", "[",
RowBox[{"s", ",", "y"}], "]"}]}]}], ";", "\[IndentingNewLine]",
RowBox[{"s", "=",
RowBox[{"s", "+", "h2"}]}], ";", "\[IndentingNewLine]",
RowBox[{"k2", "=",
RowBox[{"h", "*",
RowBox[{"f", "[",
RowBox[{"s", ",",
RowBox[{"y", "+",
RowBox[{"k1", "/", "2"}]}]}], "]"}]}]}], ";",
"\[IndentingNewLine]",
RowBox[{"k3", "=",
RowBox[{"h", "*",
RowBox[{"f", "[",
RowBox[{"s", ",",
RowBox[{"y", "+",
RowBox[{"k2", "/", "2"}]}]}], "]"}]}]}], ";",
"\[IndentingNewLine]",
RowBox[{"s", "=",
RowBox[{"s", "+", "h2"}]}], ";", "\[IndentingNewLine]",
RowBox[{"k4", "=",
RowBox[{"h", "*",
RowBox[{"f", "[",
RowBox[{"s", ",",
RowBox[{"y", "+", "k3"}]}], "]"}]}]}], ";",
"\[IndentingNewLine]",
RowBox[{"y", "=",
RowBox[{"y", "+",
RowBox[{
RowBox[{"(",
RowBox[{"k1", "+",
RowBox[{"2", " ", "k2"}], "+",
RowBox[{"2", " ", "k3"}], "+", "k4"}], ")"}], "/",
"6"}]}]}]}]}], "]"}], ";", "\[IndentingNewLine]", "y"}]}],
"]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{
RowBox[{
RowBox[{"g", "[",
RowBox[{"t_", ",", "x_"}], "]"}], ":=",
RowBox[{"{",
RowBox[{
RowBox[{"x", "[",
RowBox[{"[", "2", "]"}], "]"}], ",",
RowBox[{"(",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"-", "9.8"}], "/", "0.6"}], ")"}], "*",
RowBox[{"Sin", "[",
RowBox[{"x", "[",
RowBox[{"[", "1", "]"}], "]"}], "]"}]}], ")"}]}], "}"}]}], ";"}],
"*)"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"g", "[",
RowBox[{"t_", ",", "x_"}], "]"}], ":=",
RowBox[{"{",
RowBox[{
RowBox[{"x", "[",
RowBox[{"[", "2", "]"}], "]"}], ",",
RowBox[{
RowBox[{"-",
RowBox[{"(", "0.1", ")"}]}], "*",
RowBox[{"x", "[",
RowBox[{"[", "2", "]"}], "]"}], "*",
RowBox[{"(",
RowBox[{"Sqrt", "[",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"x", "[",
RowBox[{"[", "2", "]"}], "]"}], "^", "2"}], ")"}], "+",
RowBox[{"(",
RowBox[{
RowBox[{"x", "[",
RowBox[{"[", "4", "]"}], "]"}], "^", "2"}], ")"}]}], "]"}],
")"}]}], ",",
RowBox[{"x", "[",
RowBox[{"[", "4", "]"}], "]"}], ",",
RowBox[{
RowBox[{"-", "9.8"}], "-",
RowBox[{
RowBox[{"(", "0.1", ")"}], "*",
RowBox[{"x", "[",
RowBox[{"[", "4", "]"}], "]"}], "*",
RowBox[{"(",
RowBox[{"Sqrt", "[",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"x", "[",
RowBox[{"[", "2", "]"}], "]"}], "^", "2"}], ")"}], "+",
RowBox[{"(",
RowBox[{
RowBox[{"x", "[",
RowBox[{"[", "4", "]"}], "]"}], "^", "2"}], ")"}]}], "]"}],
")"}]}]}]}], "}"}]}], ";"}],
"\[IndentingNewLine]"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"a", "=", "20"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"dt", "=", ".001"}], ";",
RowBox[{"(*",
RowBox[{
RowBox[{
"if", " ", "we", " ", "make", " ", "larger", " ", "steps", " ", "then",
" ", "we", " ", "will", " ", "see", " ", "the", " ", "plot", " ", "has",
" ", "kinks"}], ",",
RowBox[{"not", " ", "smooth"}]}], "*)"}],
RowBox[{"n", "=", "10"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"x", "=",
RowBox[{"{",
RowBox[{"0.", ",", "20.", ",", "0.", ",", "10."}], "}"}]}], ";"}],
"\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{
"we", " ", "will", " ", "make", " ", "a", " ", "list", " ", "of", " ",
"data", " ", "so", " ", "we", " ", "can", " ", "plot"}], "*)"}],
"\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{
"a", " ", "lot", " ", "of", " ", "solvers", " ", "work", " ", "like", " ",
"this", " ", "by", " ", "making", " ", "a", " ", "list", " ", "then", " ",
"we", " ", "can", " ", "interpolate", " ", "on", " ", "this", " ", "say",
" ", "with", " ", "splines"}], "*)"}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"lst", "=",
RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"lst2", "=",
RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"For", "[",
RowBox[{
RowBox[{"t", "=", "0."}], ",",
RowBox[{"t", "<", "10"}], ",",
RowBox[{"t", "=",
RowBox[{"t", "+", "dt"}]}], ",",
RowBox[{
RowBox[{"lst", "=",
RowBox[{"Append", "[",
RowBox[{"lst", ",",
RowBox[{"{",
RowBox[{"t", ",",
RowBox[{"x", "[",
RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "]"}]}], ";",
"\[IndentingNewLine]",
RowBox[{"lst2", "=",
RowBox[{"Append", "[",
RowBox[{"lst2", ",",
RowBox[{"{",
RowBox[{"t", ",",
RowBox[{"x", "[",
RowBox[{"[", "3", "]"}], "]"}]}], "}"}]}], "]"}]}], ";",
"\[IndentingNewLine]",
RowBox[{"x", "=",
RowBox[{"RK", "[",
RowBox[{"g", ",", "t", ",", "x", ",",
RowBox[{"dt", "/", "n"}], ",", "n"}], "]"}]}]}]}], "]"}], ";"}],
"\[IndentingNewLine]"}], "\[IndentingNewLine]",
RowBox[{"ListPlot", "[",
RowBox[{"lst", ",",
RowBox[{"Joined", "\[Rule]", "True"}]}], "]"}], "\[IndentingNewLine]",
RowBox[{"ListPlot", "[",
RowBox[{"lst2", ",",
RowBox[{"Joined", "\[Rule]", "True"}]}],
"]"}], "\[IndentingNewLine]"}], "Input",
CellChangeTimes->{{3.687254780805784*^9, 3.6872548441114907`*^9}, {
3.6872548747113447`*^9, 3.6872549521481667`*^9}, {3.6872549950486264`*^9,
3.687254996836904*^9}, {3.687255032241388*^9, 3.6872550406990447`*^9}, {
3.6876907001347384`*^9, 3.687690764370719*^9}, {3.68769080928148*^9,
3.6876908657205353`*^9}, {3.6876909041408195`*^9, 3.687690910790703*^9}, {
3.6876909803850737`*^9, 3.6876910359622555`*^9}, {3.687691068123287*^9,
3.6876911115491886`*^9}, {3.687691395746663*^9, 3.6876915175624313`*^9}, {
3.6876915833026175`*^9, 3.6876917515544477`*^9}, {3.687691787317713*^9,
3.6876918959614296`*^9}, {3.687691932126685*^9, 3.6876920637616215`*^9}, {
3.687692110647338*^9, 3.6876921385539126`*^9}, {3.6880039334484644`*^9,
3.6880039591318407`*^9}, {3.688003999222077*^9, 3.688004035100151*^9},
3.6880042104852495`*^9, 3.688004848989297*^9, {3.6880050416755233`*^9,
3.6880050493533382`*^9}, {3.6880051592081704`*^9,
3.6880051632580185`*^9}, {3.6880698594044847`*^9,
3.6880698682009163`*^9}, {3.688069944612439*^9, 3.688069955692691*^9},
3.6880701243226414`*^9, {3.6880760185341616`*^9, 3.6880760208816576`*^9}, {
3.688076052624946*^9, 3.6880760571807137`*^9}, {3.688076136343485*^9,
3.6880761375664005`*^9}, {3.68807618423149*^9, 3.6880761871504765`*^9},
3.6880762816293855`*^9, {3.688107263067453*^9, 3.6881072718137755`*^9}, {
3.6881077964688454`*^9, 3.688107803448906*^9}, {3.688108242839117*^9,
3.6881082461948543`*^9}, 3.6881082849901257`*^9, {3.6881083622136917`*^9,
3.6881083761907773`*^9}, {3.6881085377312984`*^9, 3.688108540712494*^9}, {
3.6881090068405085`*^9, 3.6881090134818525`*^9}, 3.6881122279701195`*^9, {
3.690671191226962*^9, 3.6906712048509116`*^9}, {3.690671236705889*^9,
3.690671251594781*^9}, {3.6906713142345963`*^9, 3.690671326955655*^9}, {
3.690671397082982*^9, 3.6906714386028233`*^9}, {3.690671482963029*^9,
3.6906716135553246`*^9}, 3.690671730379447*^9, {3.6906718495011077`*^9,
3.6906718523084235`*^9}, {3.6906720498125963`*^9,
3.6906720733643084`*^9}, {3.690672732988019*^9, 3.690672781979849*^9},
3.6907725974128556`*^9, 3.690772642755891*^9, 3.6907726793020377`*^9, {
3.6955812802020674`*^9, 3.695581283057457*^9}}],
Cell[BoxData[
GraphicsBox[{{}, {{}, {},
{RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.003666666666666667],
AbsoluteThickness[1.6], LineBox[CompressedData["
1:eJxc22VYVFsXB3BCVFS6e4ZpTECxXcvAwu5GLMyriK2IXdiBiV3YhY0KCIIg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