9 October 2013 9:01:03.741 PM RK4_PRB FORTRAN77 version Test the RK4 library. TEST01 RK4 solves a scalar ODE. T U(T) 0.00000 0.500000 0.100000 0.552493 0.200000 0.609889 0.300000 0.671912 0.400000 0.738061 0.500000 0.807573 0.600000 0.879409 0.700000 0.952248 0.800000 1.02450 0.900000 1.09437 1.00000 1.15989 1.10000 1.21904 1.20000 1.26984 1.30000 1.31050 1.40000 1.33951 1.50000 1.35574 1.60000 1.35856 1.70000 1.34786 1.80000 1.32406 1.90000 1.28808 2.00000 1.24129 2.10000 1.18538 2.20000 1.12226 2.30000 1.05396 2.40000 0.982471 2.50000 0.909668 2.60000 0.837239 2.70000 0.766617 2.80000 0.698962 2.90000 0.635147 3.00000 0.575781 3.10000 0.521229 3.20000 0.471648 3.30000 0.427034 3.40000 0.387249 3.50000 0.352068 3.60000 0.321208 3.70000 0.294351 3.80000 0.271171 3.90000 0.251349 4.00000 0.234582 4.10000 0.220596 4.20000 0.209146 4.30000 0.200025 4.40000 0.193061 4.50000 0.188120 4.60000 0.185104 4.70000 0.183954 4.80000 0.184647 4.90000 0.187196 5.00000 0.191653 5.10000 0.198104 5.20000 0.206676 5.30000 0.217531 5.40000 0.230868 5.50000 0.246921 5.60000 0.265959 5.70000 0.288277 5.80000 0.314193 5.90000 0.344031 6.00000 0.378113 6.10000 0.416733 6.20000 0.460134 6.30000 0.508478 6.40000 0.561806 6.50000 0.620005 6.60000 0.682764 6.70000 0.749538 6.80000 0.819522 6.90000 0.891627 7.00000 0.964485 7.10000 1.03647 7.20000 1.10575 7.30000 1.17033 7.40000 1.22821 7.50000 1.27743 7.60000 1.31623 7.70000 1.34315 7.80000 1.35716 7.90000 1.35770 8.00000 1.34475 8.10000 1.31883 8.20000 1.28093 8.30000 1.23247 8.40000 1.17522 8.50000 1.11109 8.60000 1.04211 8.70000 0.970272 8.80000 0.897421 8.90000 0.825202 9.00000 0.755006 9.10000 0.687943 9.20000 0.624841 9.30000 0.566265 9.40000 0.512542 9.50000 0.463802 9.60000 0.420011 9.70000 0.381018 9.80000 0.346585 9.90000 0.316421 10.0000 0.290205 10.1000 0.267612 10.2000 0.248324 10.3000 0.232043 10.4000 0.218499 10.5000 0.207455 10.6000 0.198707 10.7000 0.192092 10.8000 0.187480 10.9000 0.184781 11.0000 0.183942 11.1000 0.184945 11.2000 0.187810 11.3000 0.192595 11.4000 0.199393 11.5000 0.208337 11.6000 0.219594 11.7000 0.233370 11.8000 0.249906 11.9000 0.269474 12.0000 0.292374 12.1000 0.318927 12.2000 0.349456 12.3000 0.384282 12.4000 0.423691 12.5000 0.467915 12.6000 0.517097 12.7000 0.571257 12.8000 0.630251 12.9000 0.693730 13.0000 0.761108 13.1000 0.831531 13.2000 0.903866 13.3000 0.976698 13.4000 1.04836 13.5000 1.11699 13.6000 1.18059 13.7000 1.23715 13.8000 1.28473 13.9000 1.32162 14.0000 1.34643 14.1000 1.35820 14.2000 1.35646 14.3000 1.34128 14.4000 1.31326 14.5000 1.27347 14.6000 1.22341 14.7000 1.16486 14.8000 1.09977 14.9000 1.03018 15.0000 0.958046 15.1000 0.885192 15.2000 0.813224 15.3000 0.743485 15.4000 0.677037 15.5000 0.614664 15.6000 0.556887 15.7000 0.503997 15.8000 0.456095 15.9000 0.413125 16.0000 0.374917 16.1000 0.341223 16.2000 0.311745 16.3000 0.286161 16.4000 0.264146 16.5000 0.245384 16.6000 0.229581 16.7000 0.216473 16.8000 0.205828 16.9000 0.197450 17.0000 0.191179 17.1000 0.186894 17.2000 0.184511 17.3000 0.183981 17.4000 0.185295 17.5000 0.188478 17.6000 0.193594 17.7000 0.200743 17.8000 0.210063 17.9000 0.221728 18.0000 0.235950 18.1000 0.252976 18.2000 0.273083 18.3000 0.296575 18.4000 0.323773 18.5000 0.355003 18.6000 0.390581 18.7000 0.430785 18.8000 0.475836 18.9000 0.525858 19.0000 0.580846 19.1000 0.640624 19.2000 0.704806 19.3000 0.772763 19.4000 0.843596 19.5000 0.916120 19.6000 0.988878 19.7000 1.06017 19.8000 1.12809 19.9000 1.19065 20.0000 1.24582 20.1000 1.29172 20.2000 1.32667 20.3000 1.34934 20.4000 1.35886 20.5000 1.35484 20.6000 1.33744 20.7000 1.30735 20.8000 1.26573 20.9000 1.21411 21.0000 1.15432 21.1000 1.08833 21.2000 1.01818 21.3000 0.945799 21.4000 0.872989 21.5000 0.801309 21.6000 0.732057 21.7000 0.666247 21.8000 0.604617 21.9000 0.547647 22.0000 0.495594 22.1000 0.448528 22.2000 0.406373 22.3000 0.368944 22.4000 0.335980 22.5000 0.307180 22.6000 0.282219 22.7000 0.260772 22.8000 0.242527 22.9000 0.227195 23.0000 0.214517 23.1000 0.204266 23.2000 0.196252 23.3000 0.190323 23.4000 0.186362 23.5000 0.184293 23.6000 0.184073 23.7000 0.185698 23.8000 0.189201 23.9000 0.194651 24.0000 0.202154 24.1000 0.211855 24.2000 0.223934 24.3000 0.238610 24.4000 0.256133 24.5000 0.276788 24.6000 0.300880 24.7000 0.328733 24.8000 0.360673 24.9000 0.397010 25.0000 0.438016 25.1000 0.483897 25.2000 0.534759 25.3000 0.590570 25.4000 0.651121 25.5000 0.715990 25.6000 0.784501 25.7000 0.855708 25.8000 0.928381 25.9000 1.00102 26.0000 1.07188 26.1000 1.13904 26.2000 1.20049 26.3000 1.25424 26.4000 1.29841 26.5000 1.33137 26.6000 1.35188 26.7000 1.35913 26.8000 1.35284 26.9000 1.33324 27.0000 1.30112 27.1000 1.25770 27.2000 1.20457 27.3000 1.14360 27.4000 1.07677 27.5000 1.00611 27.6000 0.933541 27.7000 0.860818 27.8000 0.789463 27.9000 0.720727 28.0000 0.655575 28.1000 0.594702 28.2000 0.538546 28.3000 0.487331 28.4000 0.441100 28.5000 0.399755 28.6000 0.363096 28.7000 0.330855 28.8000 0.302723 28.9000 0.278375 29.0000 0.257488 29.1000 0.239753 29.2000 0.224884 29.3000 0.212629 29.4000 0.202766 29.5000 0.195113 29.6000 0.189522 29.7000 0.185884 29.8000 0.184127 29.9000 0.184217 30.0000 0.186154 30.1000 0.189979 30.2000 0.195765 30.3000 0.203627 30.4000 0.213714 30.5000 0.226214 30.6000 0.241350 30.7000 0.259379 30.8000 0.280590 30.9000 0.305292 31.0000 0.333809 31.1000 0.366468 31.2000 0.403572 31.3000 0.445386 31.4000 0.492100 31.5000 0.543800 31.6000 0.600428 31.7000 0.661742 31.8000 0.727277 31.9000 0.796316 32.0000 0.867863 32.1000 0.940642 32.2000 1.01311 32.3000 1.08348 32.4000 1.14983 32.5000 1.21012 32.6000 1.26238 32.7000 1.30477 32.8000 1.33572 32.9000 1.35404 33.0000 1.35902 33.1000 1.35046 33.2000 1.32869 33.3000 1.29457 33.4000 1.24940 33.5000 1.19482 33.6000 1.13272 33.7000 1.06511 33.8000 0.993991 33.9000 0.921279 34.0000 0.848687 34.1000 0.777693 34.2000 0.709499 34.3000 0.645026 34.4000 0.584921 34.5000 0.529586 34.6000 0.479210 34.7000 0.433811 34.8000 0.393270 34.9000 0.357374 35.0000 0.325846 35.1000 0.298373 35.2000 0.274630 35.3000 0.254294 35.4000 0.237060 35.5000 0.222647 35.6000 0.210809 35.7000 0.201329 35.8000 0.194032 35.9000 0.188776 36.0000 0.185458 36.1000 0.184013 36.2000 0.184413 36.3000 0.186664 36.4000 0.190812 36.5000 0.196938 36.6000 0.205163 36.7000 0.215642 36.8000 0.228568 36.9000 0.244172 37.0000 0.262715 37.1000 0.284490 37.2000 0.309811 37.3000 0.339003 37.4000 0.372388 37.5000 0.410267 37.6000 0.452894 37.7000 0.500444 TEST02 RK4VEC takes a Runge Kutta step for a vector ODE. 0.00000 0.00000 1.00000 0.100000 0.999167E-01 0.995833 0.200000 0.199001 0.981701 0.300000 0.296260 0.957727 0.400000 0.390718 0.924135 0.500000 0.481427 0.881245 0.600000 0.567472 0.829471 0.700000 0.647985 0.769315 0.800000 0.722153 0.701365 0.900000 0.789222 0.626287 1.00000 0.848510 0.544821 1.10000 0.899411 0.457771 1.20000 0.941403 0.365997 1.30000 0.974049 0.270411 1.40000 0.997009 0.171960 1.50000 1.01004 0.716258E-01 1.60000 1.01298 -0.295922E-01 1.70000 1.00581 -0.130683 1.80000 0.988559 -0.230635 1.90000 0.961396 -0.328448 2.00000 0.924573 -0.423139 2.10000 0.878442 -0.513756 2.20000 0.823449 -0.599386 2.30000 0.760129 -0.679165 2.40000 0.689102 -0.752285 2.50000 0.611065 -0.818003 2.60000 0.526786 -0.875650 2.70000 0.437099 -0.924636 2.80000 0.342892 -0.964457 2.90000 0.245098 -0.994699 3.00000 0.144689 -1.01504 3.10000 0.426666E-01 -1.02527 3.20000 -0.599529E-01 -1.02526 3.30000 -0.162144 -1.01500 3.40000 -0.262884 -0.994570 3.50000 -0.361163 -0.964160 3.60000 -0.455993 -0.924056 3.70000 -0.546422 -0.874645 3.80000 -0.631537 -0.816404 3.90000 -0.710478 -0.749901 4.00000 -0.782445 -0.675788 4.10000 -0.846707 -0.594793 4.20000 -0.902609 -0.507714 4.30000 -0.949577 -0.415413 4.40000 -0.987128 -0.318804 4.50000 -1.01487 -0.218845 4.60000 -1.03251 -0.116531 4.70000 -1.03985 -0.128806E-01 4.80000 -1.03680 0.910711E-01 4.90000 -1.02338 0.194285 5.00000 -0.999706 0.295729 5.10000 -0.965992 0.394384 5.20000 -0.922561 0.489259 5.30000 -0.869832 0.579400 5.40000 -0.808316 0.663897 5.50000 -0.738614 0.741895 5.60000 -0.661409 0.812603 5.70000 -0.577460 0.875303 5.80000 -0.487597 0.929354 5.90000 -0.392707 0.974201 6.00000 -0.293732 1.00938 6.10000 -0.191654 1.03452 6.20000 -0.874897E-01 1.04936 6.30000 0.177235E-01 1.05373 6.40000 0.122935 1.04757 6.50000 0.227092 1.03092 6.60000 0.329152 1.00394 6.70000 0.428091 0.966864 6.80000 0.522913 0.920062 6.90000 0.612664 0.863981 7.00000 0.696437 0.799166 7.10000 0.773385 0.726250 7.20000 0.842727 0.645950 7.30000 0.903757 0.559056 7.40000 0.955851 0.466427 7.50000 0.998472 0.368978 7.60000 1.03118 0.267676 7.70000 1.05363 0.163529 7.80000 1.06558 0.575729E-01 7.90000 1.06689 -0.491358E-01 8.00000 1.05753 -0.155531 8.10000 1.03759 -0.260548 8.20000 1.00723 -0.363135 8.30000 0.966751 -0.462261 8.40000 0.916535 -0.556930 8.50000 0.857070 -0.646186 8.60000 0.788934 -0.729129 8.70000 0.712795 -0.804919 8.80000 0.629400 -0.872785 8.90000 0.539571 -0.932036 9.00000 0.444197 -0.982065 9.10000 0.344222 -1.02236 9.20000 0.240637 -1.05249 9.30000 0.134473 -1.07215 9.40000 0.267877E-01 -1.08112 9.50000 -0.813454E-01 -1.07929 9.60000 -0.188845 -1.06666 9.70000 -0.294636 -1.04335 9.80000 -0.397656 -1.00956 9.90000 -0.496872 -0.965625 10.0000 -0.591283 -0.911956 10.1000 -0.679939 -0.849077 10.2000 -0.761943 -0.777602 10.3000 -0.836464 -0.698231 10.4000 -0.902743 -0.611745 10.5000 -0.960106 -0.518997 10.6000 -1.00796 -0.420904 10.7000 -1.04582 -0.318438 10.8000 -1.07328 -0.212616 10.9000 -1.09005 -0.104492 11.0000 -1.09595 0.485706E-02 11.1000 -1.09090 0.114340 11.2000 -1.07493 0.222862 11.3000 -1.04818 0.329337 11.4000 -1.01091 0.432695 11.5000 -0.963460 0.531899 11.6000 -0.906300 0.625948 11.7000 -0.839981 0.713894 11.8000 -0.765151 0.794848 11.9000 -0.682544 0.867987 12.0000 -0.592974 0.932568 12.1000 -0.497324 0.987931 12.2000 -0.396541 1.03351 12.3000 -0.291625 1.06882 12.4000 -0.183617 1.09350 12.5000 -0.735922E-01 1.10729 12.6000 0.373516E-01 1.11003 12.7000 0.148107 1.10168 12.8000 0.257566 1.08229 12.9000 0.364631 1.05204 13.0000 0.468229 1.01123 13.1000 0.567316 0.960230 13.2000 0.660895 0.899545 13.3000 0.748021 0.829762 13.4000 0.827811 0.751565 13.5000 0.899456 0.665722 13.6000 0.962225 0.573077 13.7000 1.01548 0.474547 13.8000 1.05866 0.371107 13.9000 1.09133 0.263783 14.0000 1.11314 0.153642 14.1000 1.12385 0.417806E-01 14.2000 1.12334 -0.706850E-01 14.3000 1.11160 -0.182631 14.4000 1.08872 -0.292937 14.5000 1.05491 -0.400498 14.6000 1.01050 -0.504233 14.7000 0.955911 -0.603098 14.8000 0.891668 -0.696096 14.9000 0.818401 -0.782289 15.0000 0.736828 -0.860801 15.1000 0.647749 -0.930836 15.2000 0.552044 -0.991678 15.3000 0.450659 -1.04270 15.4000 0.344597 -1.08339 15.5000 0.234913 -1.11331 15.6000 0.122697 -1.13214 15.7000 0.906586E-02 -1.13968 15.8000 -0.104845 -1.13584 15.9000 -0.217897 -1.12063 16.0000 -0.328959 -1.09419 16.1000 -0.436916 -1.05676 16.2000 -0.540683 -1.00870 16.3000 -0.639217 -0.950476 16.4000 -0.731522 -0.882647 16.5000 -0.816665 -0.805878 16.6000 -0.893783 -0.720922 16.7000 -0.962091 -0.628615 16.8000 -1.02089 -0.529866 16.9000 -1.06958 -0.425655 17.0000 -1.10765 -0.317012 17.1000 -1.13471 -0.205018 17.2000 -1.15047 -0.907873E-01 17.3000 -1.15475 0.245421E-01 17.4000 -1.14748 0.139818 17.5000 -1.12873 0.253888 17.6000 -1.09866 0.365610 17.7000 -1.05755 0.473861 17.8000 -1.00580 0.577554 17.9000 -0.943902 0.675643 18.0000 -0.872461 0.767140 18.1000 -0.792176 0.851117 18.2000 -0.703834 0.926722 18.3000 -0.608307 0.993185 18.4000 -0.506536 1.04983 18.5000 -0.399530 1.09606 18.6000 -0.288351 1.13142 18.7000 -0.174102 1.15551 18.8000 -0.579213E-01 1.16809 18.9000 0.590322E-01 1.16902 19.0000 0.175590 1.15825 19.1000 0.290587 1.13588 19.2000 0.402869 1.10211 19.3000 0.511309 1.05726 19.4000 0.614817 1.00177 19.5000 0.712349 0.936165 19.6000 0.802919 0.861089 19.7000 0.885611 0.777276 19.8000 0.959583 0.685550 19.9000 1.02408 0.586815 20.0000 1.07845 0.482047 20.1000 1.12212 0.372283 20.2000 1.15464 0.258614 20.3000 1.17567 0.142168 20.4000 1.18498 0.241069E-01 20.5000 1.18245 -0.943925E-01 20.6000 1.16809 -0.212145 20.7000 1.14203 -0.327973 20.8000 1.10450 -0.440714 20.9000 1.05586 -0.549235 21.0000 0.996583 -0.652445 21.1000 0.927241 -0.749302 21.2000 0.848510 -0.838826 21.3000 0.761161 -0.920112 21.4000 0.666055 -0.992330 21.5000 0.564130 -1.05475 21.6000 0.456393 -1.10672 21.7000 0.343911 -1.14771 21.8000 0.227803 -1.17729 21.9000 0.109224 -1.19514 22.0000 -0.106462E-01 -1.20108 22.1000 -0.130609 -1.19501 22.2000 -0.249466 -1.17698 22.3000 -0.366027 -1.14715 22.4000 -0.479121 -1.10580 22.5000 -0.587612 -1.05332 22.6000 -0.690408 -0.990217 22.7000 -0.786470 -0.917107 22.8000 -0.874828 -0.834705 22.9000 -0.954584 -0.743817 23.0000 -1.02493 -0.645339 23.1000 -1.08514 -0.540243 23.2000 -1.13459 -0.429569 23.3000 -1.17279 -0.314414 23.4000 -1.19932 -0.195923 23.5000 -1.21389 -0.752750E-01 23.6000 -1.21636 0.463269E-01 23.7000 -1.20666 0.167668 23.8000 -1.18488 0.287535 23.9000 -1.15121 0.404726 24.0000 -1.10598 0.518065 24.1000 -1.04961 0.626412 24.2000 -0.982644 0.728676 24.3000 -0.905743 0.823822 24.4000 -0.819655 0.910888 24.5000 -0.725227 0.988990 24.6000 -0.623389 1.05733 24.7000 -0.515146 1.11521 24.8000 -0.401571 1.16204 24.9000 -0.283791 1.19732 25.0000 -0.162977 1.22069 25.1000 -0.403307E-01 1.23188 25.2000 0.829231E-01 1.23078 25.3000 0.205553 1.21737 25.4000 0.326332 1.19176 25.5000 0.444049 1.15419 25.6000 0.557521 1.10501 25.7000 0.665606 1.04470 25.8000 0.767216 0.973840 25.9000 0.861322 0.893125 26.0000 0.946971 0.803343 26.1000 1.02329 0.705378 26.2000 1.08951 0.600195 26.3000 1.14494 0.488834 26.4000 1.18901 0.372399 26.5000 1.22126 0.252045 26.6000 1.24136 0.128970 26.7000 1.24907 0.440021E-02 26.8000 1.24431 -0.120421 26.9000 1.22709 -0.244247 27.0000 1.19757 -0.365836 27.1000 1.15603 -0.483969 27.2000 1.10286 -0.597460 27.3000 1.03857 -0.705164 27.4000 0.963782 -0.805996 27.5000 0.879234 -0.898936 27.6000 0.785752 -0.983040 27.7000 0.684255 -1.05745 27.8000 0.575747 -1.12142 27.9000 0.461300 -1.17427 28.0000 0.342049 -1.21547 28.1000 0.219178 -1.24458 28.2000 0.939102E-01 -1.26129 28.3000 -0.325055E-01 -1.26542 28.4000 -0.158807 -1.25690 28.5000 -0.283731 -1.23580 28.6000 -0.406025 -1.20230 28.7000 -0.524463 -1.15672 28.8000 -0.637854 -1.09950 28.9000 -0.745054 -1.03119 29.0000 -0.844982 -0.952445 29.1000 -0.936627 -0.864049 29.2000 -1.01906 -0.766864 29.3000 -1.09143 -0.661848 29.4000 -1.15302 -0.550038 29.5000 -1.20317 -0.432541 29.6000 -1.24137 -0.310522 29.7000 -1.26723 -0.185194 29.8000 -1.28045 -0.578051E-01 29.9000 -1.28089 0.703742E-01 30.0000 -1.26852 0.198063 30.1000 -1.24345 0.323985 30.2000 -1.20590 0.446876 30.3000 -1.15622 0.565503 30.4000 -1.09490 0.678673 30.5000 -1.02253 0.785244 30.6000 -0.939808 0.884139 30.7000 -0.847552 0.974358 30.8000 -0.746666 1.05498 30.9000 -0.638144 1.12519 31.0000 -0.523060 1.18426 31.1000 -0.402553 1.23159 31.2000 -0.277819 1.26668 31.3000 -0.150099 1.28916 31.4000 -0.206644E-01 1.29879 31.5000 0.109192 1.29544 31.6000 0.238174 1.27913 31.7000 0.364988 1.25001 31.8000 0.488364 1.20833 31.9000 0.607061 1.15450 32.0000 0.719886 1.08903 32.1000 0.825699 1.01257 32.2000 0.923431 0.925848 32.3000 1.01209 0.829724 32.4000 1.09078 0.725142 32.5000 1.15869 0.613134 32.6000 1.21512 0.494807 32.7000 1.25950 0.371334 32.8000 1.29135 0.243942 32.9000 1.31034 0.113899 33.0000 1.31627 -0.175013E-01 33.1000 1.30903 -0.148945 33.2000 1.28870 -0.279119 33.3000 1.25544 -0.406718 33.4000 1.20957 -0.530462 33.5000 1.15153 -0.649108 33.6000 1.08187 -0.761460 33.7000 1.00128 -0.866385 33.8000 0.910543 -0.962819 33.9000 0.810548 -1.04979 34.0000 0.702279 -1.12640 34.1000 0.586807 -1.19188 34.2000 0.465274 -1.24554 34.3000 0.338885 -1.28684 34.4000 0.208896 -1.31534 34.5000 0.766015E-01 -1.33073 34.6000 -0.566797E-01 -1.33284 34.7000 -0.189616 -1.32162 34.8000 -0.320878 -1.29717 34.9000 -0.449150 -1.25970 35.0000 -0.573144 -1.20958 35.1000 -0.691613 -1.14727 35.2000 -0.803363 -1.07339 35.3000 -0.907265 -0.988645 35.4000 -1.00227 -0.893875 35.5000 -1.08740 -0.790007 35.6000 -1.16181 -0.678066 35.7000 -1.22472 -0.559156 35.8000 -1.27548 -0.434457 35.9000 -1.31358 -0.305205 36.0000 -1.33860 -0.172685 36.1000 -1.35028 -0.382170E-01 36.2000 -1.34847 0.968573E-01 36.3000 -1.33317 0.231188 36.4000 -1.30452 0.363431 36.5000 -1.26277 0.492260 36.6000 -1.20832 0.616380 36.7000 -1.14170 0.734544 36.8000 -1.06355 0.845558 36.9000 -0.974634 0.948301 37.0000 -0.875822 1.04173 37.1000 -0.768087 1.12490 37.2000 -0.652490 1.19696 37.3000 -0.530175 1.25717 37.4000 -0.402354 1.30490 37.5000 -0.270296 1.33967 37.6000 -0.135315 1.36109 37.7000 0.124442E-02 1.36894 RK4_PRB: Normal end of execution. 9 October 2013 9:01:03.749 PM