18 August 2016 9:37:59.498 AM RK4_PRB FORTRAN90 version. Test the RK4 library. RK4_TEST RK4 takes a Runge Kutta step for a scalar ODE. 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 RK4VEC_TEST RK4VEC takes a Runge Kutta step for a vector ODE. 0.00000 0.00000 1.00000 0.100000 0.998333E-01 0.995004 0.200000 0.198669 0.980067 0.300000 0.295520 0.955337 0.400000 0.389418 0.921061 0.500000 0.479425 0.877583 0.600000 0.564642 0.825336 0.700000 0.644217 0.764843 0.800000 0.717356 0.696707 0.900000 0.783326 0.621611 1.00000 0.841470 0.540303 1.10000 0.891207 0.453597 1.20000 0.932039 0.362359 1.30000 0.963558 0.267500 1.40000 0.985449 0.169968 1.50000 0.997495 0.707384E-01 1.60000 0.999574 -0.291982E-01 1.70000 0.991665 -0.128843 1.80000 0.973848 -0.227201 1.90000 0.946300 -0.323288 2.00000 0.909298 -0.416145 2.10000 0.863210 -0.504845 2.20000 0.808497 -0.588500 2.30000 0.745706 -0.666274 2.40000 0.675465 -0.737392 2.50000 0.598474 -0.801142 2.60000 0.515503 -0.856887 2.70000 0.427382 -0.904071 2.80000 0.334990 -0.942221 2.90000 0.239252 -0.970957 3.00000 0.141122 -0.989992 3.10000 0.415832E-01 -0.999135 3.20000 -0.583715E-01 -0.998295 3.30000 -0.157743 -0.987480 3.40000 -0.255538 -0.966799 3.50000 -0.350780 -0.936457 3.60000 -0.442518 -0.896760 3.70000 -0.529833 -0.848101 3.80000 -0.611855 -0.790969 3.90000 -0.687764 -0.725934 4.00000 -0.756800 -0.653646 4.10000 -0.818275 -0.574827 4.20000 -0.871574 -0.490264 4.30000 -0.916164 -0.400802 4.40000 -0.951601 -0.307336 4.50000 -0.977529 -0.210799 4.60000 -0.993690 -0.112156 4.70000 -0.999923 -0.123926E-01 4.80000 -0.996165 0.874950E-01 4.90000 -0.982453 0.186508 5.00000 -0.958925 0.283658 5.10000 -0.925816 0.377974 5.20000 -0.883456 0.468513 5.30000 -0.832270 0.554370 5.40000 -0.772767 0.634689 5.50000 -0.705543 0.708666 5.60000 -0.631270 0.775563 5.70000 -0.550689 0.834710 5.80000 -0.464606 0.885517 5.90000 -0.373881 0.927476 6.00000 -0.279420 0.960168 6.10000 -0.182167 0.983267 6.20000 -0.830945E-01 0.996541 6.30000 0.168087E-01 0.999858 6.40000 0.116544 0.993185 6.50000 0.215115 0.976588 6.60000 0.311536 0.950234 6.70000 0.404845 0.914385 6.80000 0.494108 0.869400 6.90000 0.578435 0.815728 7.00000 0.656982 0.753906 7.10000 0.728965 0.684551 7.20000 0.793664 0.608356 7.30000 0.850433 0.526082 7.40000 0.898705 0.438553 7.50000 0.937997 0.346641 7.60000 0.967918 0.251266 7.70000 0.988167 0.153380 7.80000 0.998542 0.539619E-01 7.90000 0.998941 -0.459955E-01 8.00000 0.989359 -0.145493 8.10000 0.969891 -0.243537 8.20000 0.940732 -0.339148 8.30000 0.902174 -0.431370 8.40000 0.854602 -0.519282 8.50000 0.798491 -0.602006 8.60000 0.734402 -0.678714 8.70000 0.662974 -0.748641 8.80000 0.584923 -0.811088 8.90000 0.501027 -0.865431 9.00000 0.412125 -0.911127 9.10000 0.319105 -0.947719 9.20000 0.222897 -0.974841 9.30000 0.124462 -0.992224 9.40000 0.247832E-01 -0.999692 9.50000 -0.751432E-01 -0.997172 9.60000 -0.174319 -0.984689 9.70000 -0.271753 -0.962366 9.80000 -0.366471 -0.930429 9.90000 -0.457528 -0.889194 10.0000 -0.544014 -0.839075 10.1000 -0.625064 -0.780573 10.2000 -0.699868 -0.714271 10.3000 -0.767680 -0.640833 10.4000 -0.827821 -0.560991 10.5000 -0.879691 -0.475544 10.6000 -0.922771 -0.385346 10.7000 -0.956632 -0.291298 10.8000 -0.980934 -0.194339 10.9000 -0.995435 -0.954378E-01 11.0000 -0.999989 0.441656E-02 11.1000 -0.994553 0.104227 11.2000 -0.979179 0.202996 11.3000 -0.954021 0.299736 11.4000 -0.919332 0.393482 11.5000 -0.875456 0.483296 11.6000 -0.822833 0.568281 11.7000 -0.761989 0.647588 11.8000 -0.693532 0.720425 11.9000 -0.618144 0.786064 12.0000 -0.536581 0.843848 12.1000 -0.449656 0.893201 12.2000 -0.358238 0.933629 12.3000 -0.263241 0.964729 12.4000 -0.165614 0.986190 12.5000 -0.663322E-01 0.997797 12.6000 0.336126E-01 0.999434 12.7000 0.133221 0.991085 12.8000 0.231499 0.972834 12.9000 0.327464 0.944863 13.0000 0.420157 0.907450 13.1000 0.508652 0.860971 13.2000 0.592064 0.805890 13.3000 0.669561 0.742756 13.4000 0.740368 0.672201 13.5000 0.803777 0.594929 13.6000 0.859155 0.511713 13.7000 0.905949 0.423384 13.8000 0.943691 0.330825 13.9000 0.972004 0.234961 14.0000 0.990605 0.136749 14.1000 0.999308 0.371700E-01 14.2000 0.998026 -0.627799E-01 14.3000 0.986773 -0.162103 14.4000 0.965660 -0.259806 14.5000 0.934898 -0.354913 14.6000 0.894796 -0.446474 14.7000 0.845752 -0.533574 14.8000 0.788259 -0.615342 14.9000 0.722889 -0.690963 15.0000 0.650297 -0.759679 15.1000 0.571207 -0.820805 15.2000 0.486409 -0.873730 15.3000 0.396752 -0.917925 15.4000 0.303130 -0.952948 15.5000 0.206480 -0.978450 15.6000 0.107766 -0.994175 15.7000 0.797621E-02 -0.999967 15.8000 -0.918937E-01 -0.995768 15.9000 -0.190845 -0.981619 16.0000 -0.287890 -0.957662 16.1000 -0.382059 -0.924137 16.2000 -0.472410 -0.881378 16.3000 -0.558040 -0.829812 16.4000 -0.638095 -0.769956 16.5000 -0.711775 -0.702406 16.6000 -0.778343 -0.627838 16.7000 -0.837133 -0.546997 16.8000 -0.887560 -0.460690 16.9000 -0.929118 -0.369781 17.0000 -0.961392 -0.275177 17.1000 -0.984061 -0.177823 17.2000 -0.996898 -0.786923E-01 17.3000 -0.999774 0.212244E-01 17.4000 -0.992660 0.120929 17.5000 -0.975628 0.219426 17.6000 -0.948848 0.315730 17.7000 -0.912587 0.408879 17.8000 -0.867208 0.497943 17.9000 -0.813165 0.582031 18.0000 -0.750996 0.660305 18.1000 -0.681324 0.731980 18.2000 -0.604844 0.796342 18.3000 -0.522321 0.852748 18.4000 -0.434579 0.900632 18.5000 -0.342495 0.939518 18.6000 -0.246988 0.969017 18.7000 -0.149014 0.988834 18.8000 -0.495512E-01 0.998770 18.9000 0.504069E-01 0.998727 19.0000 0.149861 0.988706 19.1000 0.247819 0.968805 19.2000 0.343299 0.939225 19.3000 0.435350 0.900260 19.4000 0.523051 0.852300 19.5000 0.605526 0.795824 19.6000 0.681951 0.731396 19.7000 0.751562 0.659661 19.8000 0.813663 0.581334 19.9000 0.867635 0.497199 20.0000 0.912937 0.408097 20.1000 0.949118 0.314916 20.2000 0.975815 0.218589 20.3000 0.992763 0.120078 20.4000 0.999791 0.203678E-01 20.5000 0.996830 -0.795465E-01 20.6000 0.983908 -0.178666 20.7000 0.961156 -0.276000 20.8000 0.928800 -0.370577 20.9000 0.887164 -0.461451 21.0000 0.836664 -0.547714 21.1000 0.777804 -0.628505 21.2000 0.711173 -0.703015 21.3000 0.637435 -0.770502 21.4000 0.557329 -0.830290 21.5000 0.471654 -0.881782 21.6000 0.381267 -0.924464 21.7000 0.287069 -0.957908 21.8000 0.190004 -0.981782 21.9000 0.910404E-01 -0.995846 22.0000 -0.883303E-02 -0.999959 22.1000 -0.108618 -0.994082 22.2000 -0.207318 -0.978272 22.3000 -0.303946 -0.952687 22.4000 -0.397538 -0.917584 22.5000 -0.487157 -0.873312 22.6000 -0.571909 -0.820315 22.7000 -0.650947 -0.759121 22.8000 -0.723481 -0.690342 22.9000 -0.788785 -0.614666 23.0000 -0.846209 -0.532848 23.1000 -0.895177 -0.445706 23.2000 -0.935202 -0.354111 23.3000 -0.965882 -0.258978 23.4000 -0.986911 -0.161257 23.5000 -0.998079 -0.619247E-01 23.6000 -0.999275 0.380263E-01 23.7000 -0.990487 0.137597 23.8000 -0.971802 0.235793 23.9000 -0.943406 0.331634 24.0000 -0.905585 0.424160 24.1000 -0.858716 0.512449 24.2000 -0.803266 0.595617 24.3000 -0.739791 0.672834 24.4000 -0.668924 0.743329 24.5000 -0.591373 0.806396 24.6000 -0.507913 0.861406 24.7000 -0.419379 0.907809 24.8000 -0.326654 0.945142 24.9000 -0.230665 0.973031 25.0000 -0.132372 0.991198 25.1000 -0.327562E-01 0.999462 25.2000 0.671871E-01 0.997739 25.3000 0.166459 0.986047 25.4000 0.264068 0.964502 25.5000 0.359038 0.933321 25.6000 0.450421 0.892814 25.7000 0.537303 0.843387 25.8000 0.618817 0.785533 25.9000 0.694148 0.719830 26.0000 0.762543 0.646935 26.1000 0.823319 0.567575 26.2000 0.875869 0.482545 26.3000 0.919667 0.392694 26.4000 0.954277 0.298918 26.5000 0.979351 0.202156 26.6000 0.994641 0.103374 26.7000 0.999992 0.355971E-02 26.8000 0.995351 -0.962906E-01 26.9000 0.980766 -0.195179 27.0000 0.956381 -0.292117 27.1000 0.922440 -0.386136 27.2000 0.879282 -0.476297 27.3000 0.827339 -0.561699 27.4000 0.767129 -0.641489 27.5000 0.699255 -0.714870 27.6000 0.624394 -0.781107 27.7000 0.543294 -0.839540 27.8000 0.456766 -0.889585 27.9000 0.365673 -0.930741 28.0000 0.270928 -0.962598 28.1000 0.173475 -0.984836 28.2000 0.742887E-01 -0.997235 28.3000 -0.256398E-01 -0.999669 28.4000 -0.125312 -0.992115 28.5000 -0.223732 -0.974649 28.6000 -0.319917 -0.947444 28.7000 -0.412905 -0.910772 28.8000 -0.501768 -0.865000 28.9000 -0.585617 -0.810586 29.0000 -0.663615 -0.748072 29.1000 -0.734982 -0.678084 29.2000 -0.799005 -0.601321 29.3000 -0.855045 -0.518549 29.4000 -0.902542 -0.430597 29.5000 -0.941021 -0.338342 29.6000 -0.970098 -0.242706 29.7000 -0.989481 -0.144645 29.8000 -0.998979 -0.451395E-01 29.9000 -0.998494 0.548174E-01 30.0000 -0.988033 0.154227 30.1000 -0.967700 0.252095 30.2000 -0.937698 0.347444 30.3000 -0.898327 0.439322 30.4000 -0.849981 0.526810 30.5000 -0.793141 0.609035 30.6000 -0.728377 0.685174 30.7000 -0.656335 0.754467 30.8000 -0.577735 0.816222 30.9000 -0.493362 0.869821 31.0000 -0.404060 0.914730 31.1000 -0.310721 0.950499 31.2000 -0.214277 0.976771 31.3000 -0.115693 0.993283 31.4000 -0.159519E-01 0.999871 31.5000 0.839482E-01 0.996468 31.6000 0.183010 0.983109 31.7000 0.280242 0.959927 31.8000 0.374675 0.927154 31.9000 0.465364 0.885117 32.0000 0.551403 0.834236 32.1000 0.631933 0.775020 32.2000 0.706149 0.708060 32.3000 0.773309 0.634026 32.4000 0.832743 0.553656 32.5000 0.883856 0.467755 32.6000 0.926138 0.377180 32.7000 0.959166 0.282836 32.8000 0.982611 0.185666 32.9000 0.996237 0.866412E-01 33.0000 0.999910 -0.132493E-01 33.1000 0.993592 -0.113007 33.2000 0.977346 -0.211636 33.3000 0.951335 -0.308151 33.4000 0.915819 -0.401586 33.5000 0.871152 -0.491009 33.6000 0.817780 -0.575526 33.7000 0.756238 -0.654293 33.8000 0.687140 -0.726522 33.9000 0.611176 -0.791492 34.0000 0.529105 -0.848553 34.1000 0.441748 -0.897136 34.2000 0.349977 -0.936756 34.3000 0.254709 -0.967015 34.4000 0.156896 -0.987613 34.5000 0.575159E-01 -0.998342 34.6000 -0.424392E-01 -0.999097 34.7000 -0.141970 -0.989868 34.8000 -0.240083 -0.970750 34.9000 -0.335797 -0.941932 35.0000 -0.428155 -0.903702 35.1000 -0.516236 -0.856444 35.2000 -0.599159 -0.800627 35.3000 -0.676095 -0.736812 35.4000 -0.746275 -0.665634 35.5000 -0.808999 -0.587805 35.6000 -0.863640 -0.504104 35.7000 -0.909652 -0.415365 35.8000 -0.946575 -0.322476 35.9000 -0.974040 -0.226366 36.0000 -0.991773 -0.127993 36.1000 -0.999596 -0.283416E-01 36.2000 -0.997431 0.715929E-01 36.3000 -0.985301 0.170812 36.4000 -0.963326 0.268325 36.5000 -0.931726 0.363156 36.6000 -0.890816 0.454359 36.7000 -0.841005 0.541022 36.8000 -0.782792 0.622280 36.9000 -0.716757 0.697320 37.0000 -0.643560 0.765392 37.1000 -0.563933 0.825817 37.2000 -0.478672 0.877991 37.3000 -0.388628 0.921392 37.4000 -0.294701 0.955587 37.5000 -0.197829 0.980234 37.6000 -0.989805E-01 0.995087 37.7000 0.856850E-03 0.999997 RK4_PRB Normal end of execution. 18 August 2016 9:37:59.499 AM