##############ECHO OF PROBLEM################# ##############temp/mtest2postode.ode################# diff ( y1 , x , 1 ) = m1 * y2 + 1.0; diff ( y2 , x , 1 ) = y1 - 1.0; ! // BEGIN FIRST INPUT BLOCK Digits = 32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start = 0.1; x_end = 10.0; array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); // # testing comment glob_h = 0.00001 ; glob_look_poles = true; glob_max_iter = 10; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_h = 0.005 ; glob_display_interval = 0.1; glob_look_poles = true; glob_max_iter = 10000; glob_max_minutes = 10; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y1 (double x) { return(1.0 + cos(x)); } double exact_soln_y2 (double x) { return(1.0 + sin(x)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y1[1] (analytic) = 1.995004165278026 y1[1] (numeric) = 1.995004165278026 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 y2[1] (analytic) = 1.099833416646828 y2[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 x[1] = 0.1 y1[1] (analytic) = 1.995004165278026 y1[1] (numeric) = 1.995004165278026 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 y2[1] (analytic) = 1.099833416646828 y2[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.2000000000000001 y1[1] (analytic) = 1.980066577841242 y1[1] (numeric) = 1.980066577841227 absolute error = 1.509903313490213e-14 relative error = 7.625517901202989e-13 % Correct digits = 14 h = 0.005 y2[1] (analytic) = 1.198669330795061 y2[1] (numeric) = 1.198669330795058 absolute error = 3.33066907387547e-15 relative error = 2.77863876909763e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.3000000000000002 y1[1] (analytic) = 1.955336489125606 y1[1] (numeric) = 1.955336489125577 absolute error = 2.864375403532904e-14 relative error = 1.464901524347763e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.29552020666134 y2[1] (numeric) = 1.29552020666133 absolute error = 9.769962616701378e-15 relative error = 7.541343289333449e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.4000000000000002 y1[1] (analytic) = 1.921060994002885 y1[1] (numeric) = 1.921060994002844 absolute error = 4.107825191113079e-14 relative error = 2.138310654339854e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.389418342308651 y2[1] (numeric) = 1.389418342308632 absolute error = 1.865174681370263e-14 relative error = 1.342414033681964e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5000000000000003 y1[1] (analytic) = 1.877582561890373 y1[1] (numeric) = 1.877582561890321 absolute error = 5.195843755245733e-14 relative error = 2.767305076595138e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.479425538604203 y2[1] (numeric) = 1.479425538604173 absolute error = 2.997602166487923e-14 relative error = 2.026193335364534e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.6000000000000004 y1[1] (analytic) = 1.825335614909678 y1[1] (numeric) = 1.825335614909617 absolute error = 6.128431095930864e-14 relative error = 3.357427010064729e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.564642473395036 y2[1] (numeric) = 1.564642473394992 absolute error = 4.39648317751562e-14 relative error = 2.809896351577317e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.7000000000000005 y1[1] (analytic) = 1.764842187284488 y1[1] (numeric) = 1.76484218728442 absolute error = 6.772360450213455e-14 relative error = 3.837374525046849e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.644217687237691 y2[1] (numeric) = 1.644217687237632 absolute error = 5.928590951498336e-14 relative error = 3.605721430632735e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.8000000000000006 y1[1] (analytic) = 1.696706709347165 y1[1] (numeric) = 1.696706709347093 absolute error = 7.194245199571014e-14 relative error = 4.240123033602617e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.717356090899523 y2[1] (numeric) = 1.717356090899446 absolute error = 7.704947790898586e-14 relative error = 4.486517287665635e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.9000000000000007 y1[1] (analytic) = 1.621609968270664 y1[1] (numeric) = 1.621609968270591 absolute error = 7.260858581048524e-14 relative error = 4.477561635114844e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.783326909627484 y2[1] (numeric) = 1.783326909627388 absolute error = 9.570122472268849e-14 relative error = 5.366443146572569e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.000000000000001 y1[1] (analytic) = 1.540302305868139 y1[1] (numeric) = 1.540302305868069 absolute error = 7.038813976123492e-14 relative error = 4.569761370418973e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.841470984807897 y2[1] (numeric) = 1.841470984807781 absolute error = 1.156852391659413e-13 relative error = 6.282218949977626e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.104999999999998 y1[1] (analytic) = 1.449134433252363 y1[1] (numeric) = 1.449134433252297 absolute error = 6.639133687258436e-14 relative error = 4.581447749024847e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.893464191149863 y2[1] (numeric) = 1.893464191149727 absolute error = 1.354472090042691e-13 relative error = 7.153407475956264e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.204999999999996 y1[1] (analytic) = 1.357693049001803 y1[1] (numeric) = 1.357693049001743 absolute error = 5.972999872483342e-14 relative error = 4.399374274527503e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.933839216726195 y2[1] (numeric) = 1.93383921672604 absolute error = 1.547650896327468e-13 relative error = 8.002996748341329e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.304999999999994 y1[1] (analytic) = 1.262677714043219 y1[1] (numeric) = 1.262677714043169 absolute error = 4.996003610813204e-14 relative error = 3.956673627204131e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.964883629535204 y2[1] (numeric) = 1.96488362953503 absolute error = 1.740829702612245e-13 relative error = 8.859708923444191e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.404999999999992 y1[1] (analytic) = 1.165037790195623 y1[1] (numeric) = 1.165037790195587 absolute error = 3.641531520770513e-14 relative error = 3.125676738914244e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.98628724406602 y2[1] (numeric) = 1.986287244065827 absolute error = 1.929567616798522e-13 relative error = 9.714443983683899e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.50499999999999 y1[1] (analytic) = 1.065748863302634 y1[1] (numeric) = 1.065748863302614 absolute error = 1.976196983832779e-14 relative error = 1.85428017038533e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.997836202477346 y2[1] (numeric) = 1.997836202477136 absolute error = 2.104982854689297e-13 relative error = 1.053631349796889e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.604999999999988 y1[1] (analytic) = 0.9658029955012084 y1[1] (numeric) = 0.9658029955012082 absolute error = 2.220446049250313e-16 relative error = 2.299067262778576e-14 % Correct digits = 15 h = 0.005 y2[1] (analytic) = 1.999415111394314 y2[1] (numeric) = 1.999415111394087 absolute error = 2.26929586233382e-13 relative error = 1.134979849557755e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.704999999999986 y1[1] (analytic) = 0.8661988128647083 y1[1] (numeric) = 0.8661988128647311 absolute error = 2.275957200481571e-14 relative error = 2.627522881213014e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.991008194880944 y2[1] (numeric) = 1.991008194880703 absolute error = 2.40918396343659e-13 relative error = 1.210032168441502e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.804999999999984 y1[1] (analytic) = 0.7679315274612719 y1[1] (numeric) = 0.7679315274613205 absolute error = 4.862776847858186e-14 relative error = 6.332305256347772e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.972699452068079 y2[1] (numeric) = 1.972699452067826 absolute error = 2.529088050096107e-13 relative error = 1.282044280716324e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.904999999999981 y1[1] (analytic) = 0.6719829935238044 y1[1] (numeric) = 0.6719829935238815 absolute error = 7.704947790898586e-14 relative error = 1.146598629006174e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.944671817861841 y2[1] (numeric) = 1.944671817861579 absolute error = 2.62234678416462e-13 relative error = 1.348477804881175e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.004999999999979 y1[1] (analytic) = 0.5793118970870402 y1[1] (numeric) = 0.5793118970871481 absolute error = 1.079136779935652e-13 relative error = 1.862790640692667e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.907205335118514 y2[1] (numeric) = 1.907205335118246 absolute error = 2.677857935395878e-13 relative error = 1.40407426829554e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.104999999999977 y1[1] (analytic) = 0.4908441771135841 y1[1] (numeric) = 0.4908441771137246 absolute error = 1.404987237663136e-13 relative error = 2.862389538621365e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.860674356548896 y2[1] (numeric) = 1.860674356548627 absolute error = 2.69784194983913e-13 relative error = 1.449926979615594e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.204999999999975 y1[1] (analytic) = 0.4074637738178705 y1[1] (numeric) = 0.4074637738180449 absolute error = 1.743605260173808e-13 relative error = 4.279166326460154e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.80554380430976 y2[1] (numeric) = 1.805543804309492 absolute error = 2.673417043297377e-13 relative error = 1.480671383832416e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.304999999999973 y1[1] (analytic) = 0.3300037966277331 y1[1] (numeric) = 0.3300037966279423 absolute error = 2.091660178393795e-13 relative error = 6.33829125533768e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.742364524655339 y2[1] (numeric) = 1.742364524655079 absolute error = 2.606803661819868e-13 relative error = 1.496129899875874e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.404999999999971 y1[1] (analytic) = 0.2592382000303916 y1[1] (numeric) = 0.2592382000306359 absolute error = 2.442490654175344e-13 relative error = 9.421800698697186e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.671767784063649 y2[1] (numeric) = 1.6717677840634 absolute error = 2.493560913308102e-13 relative error = 1.491571339679054e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.504999999999969 y1[1] (analytic) = 0.1958740504750504 y1[1] (numeric) = 0.1958740504753295 absolute error = 2.7913782396638e-13 relative error = 1.425088332473808e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 1.594458961830502 y2[1] (numeric) = 1.594458961830267 absolute error = 2.344791028008331e-13 relative error = 1.470587255075175e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.604999999999967 y1[1] (analytic) = 0.1405444615986633 y1[1] (numeric) = 0.1405444615989767 absolute error = 3.133604487004504e-13 relative error = 2.229617909777747e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 1.511210502152752 y2[1] (numeric) = 1.511210502152537 absolute error = 2.147171329625053e-13 relative error = 1.420828750572049e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.704999999999965 y1[1] (analytic) = 0.09380226836375276 y1[1] (numeric) = 0.09380226836409905 absolute error = 3.462924391683941e-13 relative error = 3.69172777171569e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 1.422854196121216 y2[1] (numeric) = 1.422854196121026 absolute error = 1.900701818158268e-13 relative error = 1.335837377673477e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.804999999999962 y1[1] (analytic) = 0.05611450331420715 y1[1] (numeric) = 0.05611450331458448 absolute error = 3.773301116005712e-13 relative error = 6.724288540660365e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 1.330272870739051 y2[1] (numeric) = 1.33027287073889 absolute error = 1.612043831755727e-13 relative error = 1.211814408317697e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2.90499999999996 y1[1] (analytic) = 0.02785773014048269 y1[1] (numeric) = 0.02785773014088862 absolute error = 4.059287628255248e-13 relative error = 1.457149454670147e-09 % Correct digits = 10 h = 0.005 y2[1] (analytic) = 1.234391568006158 y2[1] (numeric) = 1.23439156800603 absolute error = 1.283417816466681e-13 relative error = 1.039716934019334e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.004999999999958 y1[1] (analytic) = 0.009314281179683871 y1[1] (numeric) = 0.009314281180115354 absolute error = 4.314829743501392e-13 relative error = 4.632488176235021e-09 % Correct digits = 10 h = 0.005 y2[1] (analytic) = 1.136168302205299 y2[1] (numeric) = 1.136168302205208 absolute error = 9.037215420448774e-14 relative error = 7.954116835426206e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.104999999999956 y1[1] (analytic) = 0.0006694364441777027 y1[1] (numeric) = 0.0006694364446311701 absolute error = 4.53467450221845e-13 relative error = 6.773868590002721e-08 % Correct digits = 9 h = 0.005 y2[1] (analytic) = 1.03658448774006 y2[1] (numeric) = 1.036584487740011 absolute error = 4.907185768843192e-14 relative error = 4.73399498726991e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.204999999999954 y1[1] (analytic) = 0.002009572364955621 y1[1] (numeric) = 0.002009572365426972 absolute error = 4.713512566367761e-13 relative error = 2.345530147888878e-08 % Correct digits = 9 h = 0.005 y2[1] (analytic) = 0.9366351331665469 y2[1] (numeric) = 0.9366351331665426 absolute error = 4.329869796038111e-15 relative error = 4.622792422274212e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.304999999999952 y1[1] (analytic) = 0.01332129874688725 y1[1] (numeric) = 0.01332129874737193 absolute error = 4.8467306557054e-13 relative error = 3.638331928287339e-09 % Correct digits = 10 h = 0.005 y2[1] (analytic) = 0.8373188993967933 y2[1] (numeric) = 0.8373188993968367 absolute error = 4.340972026284362e-14 relative error = 5.184371246620146e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.40499999999995 y1[1] (analytic) = 0.03449159255912395 y1[1] (numeric) = 0.03449159255961695 absolute error = 4.930014729787047e-13 relative error = 1.429338097780274e-09 % Correct digits = 10 h = 0.005 y2[1] (analytic) = 0.7396281214090444 y2[1] (numeric) = 0.7396281214091385 absolute error = 9.403589018575076e-14 relative error = 1.271394197486781e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.504999999999947 y1[1] (analytic) = 0.06530892722386258 y1[1] (numeric) = 0.06530892722435851 absolute error = 4.959227473122496e-13 relative error = 7.593490942093584e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 0.6445388931646763 y2[1] (numeric) = 0.644538893164823 absolute error = 1.467714838554457e-13 relative error = 2.277154806512915e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.604999999999945 y1[1] (analytic) = 0.1054653861199896 y1[1] (numeric) = 0.1054653861204827 absolute error = 4.931055563872633e-13 relative error = 4.675520324993166e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 0.5530013147999866 y2[1] (numeric) = 0.5530013148001875 absolute error = 2.009503674571533e-13 relative error = 3.633813556660972e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.704999999999943 y1[1] (analytic) = 0.1545597391841753 y1[1] (numeric) = 0.1545597391846596 absolute error = 4.842792833414933e-13 relative error = 3.133282224062374e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 0.4659299995396949 y2[1] (numeric) = 0.4659299995399507 absolute error = 2.558508960248673e-13 relative error = 5.491187437547045e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.804999999999941 y1[1] (analytic) = 0.212101451869038 y1[1] (numeric) = 0.2121014518695074 absolute error = 4.693467836602849e-13 relative error = 2.212840975506773e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 0.3841949351839317 y2[1] (numeric) = 0.3841949351842426 absolute error = 3.109179580462751e-13 relative error = 8.092713608976247e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3.904999999999939 y1[1] (analytic) = 0.2775155864021918 y1[1] (numeric) = 0.27751558640264 absolute error = 4.481415238899444e-13 relative error = 1.614833709701882e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 0.3086127914777196 y2[1] (numeric) = 0.3086127914780852 absolute error = 3.65596442009064e-13 relative error = 1.184644486894052e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE Finished! Maximum Time Reached before Solution Completed! diff ( y1 , x , 1 ) = m1 * y2 + 1.0; diff ( y2 , x , 1 ) = y1 - 1.0; Iterations = 778 Total Elapsed Time = 10 Minutes 6 Seconds Elapsed Time(since restart) = 10 Minutes 5 Seconds Expected Time Remaining = 15 Minutes 34 Seconds Optimized Time Remaining = 15 Minutes 32 Seconds Time to Timeout Unknown Percent Done = 39.34 %