09 October 2013 10:11:00 PM
RK4_PRB
C++ version
Test the RK4 library.
TEST01
RK4 takes one Runge Kutta step for a scalar ODE.
T U[T]
0 0.5
0.1 0.552493
0.2 0.609889
0.3 0.671912
0.4 0.738061
0.5 0.807573
0.6 0.879409
0.7 0.952248
0.8 1.0245
0.9 1.09437
1 1.15989
1.1 1.21904
1.2 1.26984
1.3 1.3105
1.4 1.33951
1.5 1.35574
1.6 1.35856
1.7 1.34786
1.8 1.32406
1.9 1.28808
2 1.24129
2.1 1.18538
2.2 1.12226
2.3 1.05396
2.4 0.982471
2.5 0.909668
2.6 0.837239
2.7 0.766617
2.8 0.698962
2.9 0.635147
3 0.575781
3.1 0.521229
3.2 0.471648
3.3 0.427034
3.4 0.387249
3.5 0.352068
3.6 0.321208
3.7 0.294351
3.8 0.271171
3.9 0.251349
4 0.234582
4.1 0.220596
4.2 0.209146
4.3 0.200025
4.4 0.193061
4.5 0.18812
4.6 0.185104
4.7 0.183954
4.8 0.184647
4.9 0.187196
5 0.191653
5.1 0.198104
5.2 0.206676
5.3 0.217531
5.4 0.230868
5.5 0.246921
5.6 0.265959
5.7 0.288277
5.8 0.314193
5.9 0.344031
6 0.378113
6.1 0.416733
6.2 0.460134
6.3 0.508478
6.4 0.561806
6.5 0.620005
6.6 0.682764
6.7 0.749538
6.8 0.819522
6.9 0.891627
7 0.964485
7.1 1.03647
7.2 1.10575
7.3 1.17033
7.4 1.22821
7.5 1.27743
7.6 1.31623
7.7 1.34315
7.8 1.35716
7.9 1.3577
8 1.34475
8.1 1.31883
8.2 1.28093
8.3 1.23247
8.4 1.17522
8.5 1.11109
8.6 1.04211
8.7 0.970272
8.8 0.897421
8.9 0.825202
9 0.755006
9.1 0.687943
9.2 0.624841
9.3 0.566265
9.4 0.512542
9.5 0.463802
9.6 0.420011
9.7 0.381018
9.8 0.346585
9.9 0.316421
10 0.290205
10.1 0.267612
10.2 0.248324
10.3 0.232043
10.4 0.218499
10.5 0.207455
10.6 0.198707
10.7 0.192092
10.8 0.18748
10.9 0.184781
11 0.183942
11.1 0.184945
11.2 0.18781
11.3 0.192595
11.4 0.199393
11.5 0.208337
11.6 0.219594
11.7 0.23337
11.8 0.249906
11.9 0.269474
12 0.292374
12.1 0.318927
12.2 0.349456
12.3 0.384282
12.4 0.423691
12.5 0.467915
12.6 0.517097
12.7 0.571257
12.8 0.630251
12.9 0.69373
13 0.761108
13.1 0.831531
13.2 0.903866
13.3 0.976698
13.4 1.04836
13.5 1.11699
13.6 1.18059
13.7 1.23715
13.8 1.28473
13.9 1.32162
14 1.34643
14.1 1.3582
14.2 1.35646
14.3 1.34128
14.4 1.31326
14.5 1.27347
14.6 1.22341
14.7 1.16486
14.8 1.09977
14.9 1.03018
15 0.958046
15.1 0.885192
15.2 0.813224
15.3 0.743485
15.4 0.677037
15.5 0.614664
15.6 0.556887
15.7 0.503997
15.8 0.456095
15.9 0.413125
16 0.374917
16.1 0.341223
16.2 0.311745
16.3 0.286161
16.4 0.264146
16.5 0.245384
16.6 0.229581
16.7 0.216473
16.8 0.205828
16.9 0.19745
17 0.191179
17.1 0.186894
17.2 0.184511
17.3 0.183981
17.4 0.185295
17.5 0.188478
17.6 0.193594
17.7 0.200743
17.8 0.210063
17.9 0.221728
18 0.23595
18.1 0.252976
18.2 0.273083
18.3 0.296575
18.4 0.323773
18.5 0.355003
18.6 0.390581
18.7 0.430785
18.8 0.475836
18.9 0.525858
19 0.580846
19.1 0.640624
19.2 0.704806
19.3 0.772763
19.4 0.843596
19.5 0.91612
19.6 0.988878
19.7 1.06017
19.8 1.12809
19.9 1.19065
20 1.24582
20.1 1.29172
20.2 1.32667
20.3 1.34934
20.4 1.35886
20.5 1.35484
20.6 1.33744
20.7 1.30735
20.8 1.26573
20.9 1.21411
21 1.15432
21.1 1.08833
21.2 1.01818
21.3 0.945799
21.4 0.872989
21.5 0.801309
21.6 0.732057
21.7 0.666247
21.8 0.604617
21.9 0.547647
22 0.495594
22.1 0.448528
22.2 0.406373
22.3 0.368944
22.4 0.33598
22.5 0.30718
22.6 0.282219
22.7 0.260772
22.8 0.242527
22.9 0.227195
23 0.214517
23.1 0.204266
23.2 0.196252
23.3 0.190323
23.4 0.186362
23.5 0.184293
23.6 0.184073
23.7 0.185698
23.8 0.189201
23.9 0.194651
24 0.202154
24.1 0.211855
24.2 0.223934
24.3 0.23861
24.4 0.256133
24.5 0.276788
24.6 0.30088
24.7 0.328733
24.8 0.360673
24.9 0.39701
25 0.438016
25.1 0.483897
25.2 0.534759
25.3 0.59057
25.4 0.651121
25.5 0.71599
25.6 0.784501
25.7 0.855708
25.8 0.928381
25.9 1.00102
26 1.07188
26.1 1.13904
26.2 1.20049
26.3 1.25424
26.4 1.29841
26.5 1.33137
26.6 1.35188
26.7 1.35913
26.8 1.35284
26.9 1.33324
27 1.30112
27.1 1.2577
27.2 1.20457
27.3 1.1436
27.4 1.07677
27.5 1.00611
27.6 0.933541
27.7 0.860818
27.8 0.789463
27.9 0.720727
28 0.655575
28.1 0.594702
28.2 0.538546
28.3 0.487331
28.4 0.4411
28.5 0.399755
28.6 0.363096
28.7 0.330855
28.8 0.302723
28.9 0.278375
29 0.257488
29.1 0.239753
29.2 0.224884
29.3 0.212629
29.4 0.202766
29.5 0.195113
29.6 0.189522
29.7 0.185884
29.8 0.184127
29.9 0.184217
30 0.186154
30.1 0.189979
30.2 0.195765
30.3 0.203627
30.4 0.213714
30.5 0.226214
30.6 0.24135
30.7 0.259379
30.8 0.28059
30.9 0.305292
31 0.333809
31.1 0.366468
31.2 0.403572
31.3 0.445386
31.4 0.4921
31.5 0.5438
31.6 0.600428
31.7 0.661742
31.8 0.727277
31.9 0.796316
32 0.867863
32.1 0.940642
32.2 1.01311
32.3 1.08348
32.4 1.14983
32.5 1.21012
32.6 1.26238
32.7 1.30477
32.8 1.33572
32.9 1.35404
33 1.35902
33.1 1.35046
33.2 1.32869
33.3 1.29457
33.4 1.2494
33.5 1.19482
33.6 1.13272
33.7 1.06511
33.8 0.993991
33.9 0.921279
34 0.848687
34.1 0.777693
34.2 0.709499
34.3 0.645026
34.4 0.584921
34.5 0.529586
34.6 0.47921
34.7 0.433811
34.8 0.39327
34.9 0.357374
35 0.325846
35.1 0.298373
35.2 0.27463
35.3 0.254294
35.4 0.23706
35.5 0.222647
35.6 0.210809
35.7 0.201329
35.8 0.194032
35.9 0.188776
36 0.185458
36.1 0.184013
36.2 0.184413
36.3 0.186664
36.4 0.190812
36.5 0.196938
36.6 0.205163
36.7 0.215642
36.8 0.228568
36.9 0.244172
37 0.262715
37.1 0.28449
37.2 0.309811
37.3 0.339003
37.4 0.372388
37.5 0.410267
37.6 0.452894
37.7 0.500444
TEST02
RK4VEC takes a Runge Kutta step for a vector ODE.
T U[0] U[1]
0 0 1
0.2 0.198667 0.980067
0.4 0.389413 0.921062
0.6 0.564635 0.825339
0.8 0.717347 0.696713
1 0.841462 0.540312
1.2 0.932031 0.362371
1.4 0.985444 0.169985
1.6 0.999571 -0.0291784
1.8 0.973849 -0.227178
2 0.909304 -0.416121
2.2 0.808509 -0.588475
2.4 0.675483 -0.737368
2.6 0.515528 -0.856866
2.8 0.335021 -0.942204
3 0.141158 -0.98998
3.2 -0.0583317 -0.99829
3.4 -0.255496 -0.966802
3.6 -0.442474 -0.896772
3.8 -0.611813 -0.790992
4 -0.756761 -0.653678
4.2 -0.871541 -0.490304
4.4 -0.951575 -0.307385
4.6 -0.993674 -0.112211
4.8 -0.99616 0.0874352
5 -0.958932 0.283596
5.2 -0.883477 0.468451
5.4 -0.7728 0.63463
5.6 -0.631316 0.77551
5.8 -0.464664 0.885473
6 -0.279488 0.960136
6.2 -0.0831695 0.996522
6.4 0.116464 0.993181
6.6 0.311454 0.950246
6.8 0.494028 0.869429
7 0.656907 0.753951
7.2 0.793598 0.608417
7.4 0.898651 0.438628
7.6 0.967878 0.251352
7.8 0.998521 0.0540569
8 0.989356 -0.145393
8.2 0.94075 -0.339047
8.4 0.85464 -0.519185
8.6 0.73446 -0.678624
8.8 0.585 -0.81101
9 0.412218 -0.911063
9.2 0.223003 -0.974797
9.4 0.0248984 -0.999669
9.6 -0.174199 -0.984689
9.8 -0.366351 -0.930453
10 -0.543899 -0.839124
10.2 -0.699763 -0.714343
10.4 -0.827731 -0.561085
10.6 -0.9227 -0.385458
10.8 -0.980885 -0.194465
11 -0.999967 0.00428102
11.2 -0.979183 0.202856
11.4 -0.919364 0.393343
11.6 -0.822894 0.56815
11.8 -0.693619 0.720306
12 -0.536692 0.843747
12.2 -0.358369 0.933551
12.4 -0.16576 0.986138
12.6 0.0334566 0.999412
12.8 0.23134 0.972844
13 0.42 0.907492
13.2 0.591916 0.805963
13.4 0.740236 0.672304
13.6 0.859045 0.511842
13.8 0.943607 0.330976
14 0.990552 0.136915
14.2 0.998007 -0.0626035
14.4 0.965676 -0.259626
14.6 0.894848 -0.446299
14.8 0.788346 -0.615179
15 0.650416 -0.759535
15.2 0.486557 -0.87361
15.4 0.303301 -0.952859
15.6 0.107954 -0.994121
15.8 -0.0916969 -0.995752
16 -0.287692 -0.957686
16.2 -0.472217 -0.881441
16.4 -0.637918 -0.770058
16.6 -0.778187 -0.627975
16.8 -0.887432 -0.460857
17 -0.9613 -0.275368
17.2 -0.996844 -0.0789006
17.4 -0.992649 0.120712
17.6 -0.948881 0.315512
17.8 -0.867285 0.497734
18 -0.751114 0.660113
18.2 -0.604999 0.796176
18.4 -0.434766 0.900498
18.6 -0.2472 0.968922
18.8 -0.0497804 0.998719
19 0.149624 0.9887
19.2 0.343063 0.939267
19.4 0.522826 0.852389
19.6 0.681746 0.73153
19.8 0.813487 0.581508
20 0.912798 0.408304
20.2 0.975719 0.218823
20.4 0.999742 0.020618
20.6 0.98391 -0.178408
20.8 0.928854 -0.370322
21 0.836768 -0.547473
21.2 0.711324 -0.702798
21.4 0.557522 -0.830105
21.6 0.381495 -0.924319
21.8 0.190259 -0.981685
22 -0.00856175 -0.999915
22.2 -0.207041 -0.978282
22.4 -0.397266 -0.91765
22.6 -0.571653 -0.820434
22.8 -0.723251 -0.690512
23 -0.846016 -0.533062
23.2 -0.935054 -0.354361
23.4 -0.986815 -0.161533
23.6 -0.999236 0.037734
23.8 -0.971821 0.235497
24 -0.905664 0.423871
24.2 -0.803402 0.595347
24.4 -0.669112 0.743089
24.6 -0.508147 0.861207
24.8 -0.326925 0.944992
25 -0.13267 0.991104
25.2 0.0668739 0.997706
25.4 0.263752 0.964532
25.6 0.450115 0.892907
25.8 0.618533 0.785686
26 0.762294 0.647143
26.2 0.875664 0.482801
26.4 0.954126 0.299212
26.6 0.99455 0.103694
26.8 0.995326 -0.0959566
27 0.956422 -0.291782
27.2 0.87939 -0.475975
27.4 0.767301 -0.641193
27.6 0.624622 -0.780849
27.8 0.457043 -0.889376
28 0.271243 -0.962447
28.2 0.0746304 -0.997149
28.4 -0.124957 -0.992099
28.6 -0.319564 -0.947498
28.8 -0.50143 -0.865125
29 -0.663306 -0.748262
29.2 -0.798739 -0.60157
29.4 -0.90233 -0.430896
29.6 -0.969948 -0.243044
29.8 -0.998898 -0.0455032
30 -0.988027 0.153852
30.2 -0.937767 0.347073
30.4 -0.850122 0.526458
30.6 -0.728587 0.684855
30.8 -0.578006 0.815949
31 -0.404383 0.914515
31.2 -0.214638 0.976623
31.4 -0.0163374 0.999797
31.6 0.182615 0.983114
31.8 0.374286 0.927237
32 0.551037 0.834396
32.2 0.705819 0.708291
32.4 0.832464 0.55395
32.6 0.925922 0.377525
32.8 0.982467 0.18605
33 0.999845 -0.0128421
33.2 0.977363 -0.211222
33.4 0.915918 -0.401181
33.6 0.81796 -0.575147
33.8 0.687392 -0.726183
34 0.529422 -0.84827
34.2 0.350346 -0.93654
34.4 0.157303 -0.987473
34.6 -0.0420105 -0.999041
34.8 -0.239649 -0.97078
35 -0.427734 -0.903819
35.2 -0.598766 -0.800827
35.4 -0.745929 -0.665908
35.6 -0.863353 -0.504444
35.8 -0.94636 -0.322869
36 -0.991639 -0.128423
36.2 -0.997386 0.0711428
36.4 -0.963371 0.267872
36.6 -0.890951 0.453922
36.8 -0.783012 0.621876
37 -0.643858 0.765038
37.2 -0.479036 0.877702
37.4 -0.295117 0.955375
37.6 -0.0994331 0.994961
37.8 0.100214 0.994882
RK4_PRB
Normal end of execution.
09 October 2013 10:11:00 PM