##############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 x[1] = 4.004999999999937 y1[1] (analytic) = 0.3501485463744196 y1[1] (numeric) = 0.3501485463748402 absolute error = 4.206079928792406e-13 relative error = 1.201227299768589e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 0.2399387602168361 y2[1] (numeric) = 0.239938760217255 absolute error = 4.188593916154559e-13 relative error = 1.745692906127075e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.104999999999935 y1[1] (analytic) = 0.4292746072589433 y1[1] (numeric) = 0.42927460725933 absolute error = 3.86690679476942e-13 relative error = 9.00800263835978e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.1788590096210234 y2[1] (numeric) = 0.1788590096214936 absolute error = 4.702072065043694e-13 relative error = 2.628926591401077e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.204999999999933 y1[1] (analytic) = 0.5141031676110031 y1[1] (numeric) = 0.5141031676113498 absolute error = 3.467226505904364e-13 relative error = 6.744223191652937e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.1259838283679535 y2[1] (numeric) = 0.1259838283684724 absolute error = 5.188904861341825e-13 relative error = 4.11870708213986e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.30499999999993 y1[1] (analytic) = 0.6037866484961552 y1[1] (numeric) = 0.6037866484964558 absolute error = 3.006483950684924e-13 relative error = 4.97938130658096e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.08184152779049592 y2[1] (numeric) = 0.08184152779106013 absolute error = 5.642153411145046e-13 relative error = 6.893998149189313e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.404999999999928 y1[1] (analytic) = 0.6974289622188125 y1[1] (numeric) = 0.6974289622190615 absolute error = 2.490230244234226e-13 relative error = 3.570586223307625e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.0468731631645161 y2[1] (numeric) = 0.04687316316512149 absolute error = 6.0539073754029e-13 relative error = 1.291550850569826e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.504999999999926 y1[1] (analytic) = 0.7940944657342917 y1[1] (numeric) = 0.7940944657344835 absolute error = 1.918465386552271e-13 relative error = 2.415915825302074e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.02142812683035223 y2[1] (numeric) = 0.02142812683099395 absolute error = 6.417123776802924e-13 relative error = 2.994719896707574e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.604999999999924 y1[1] (analytic) = 0.8928173092848333 y1[1] (numeric) = 0.8928173092849634 absolute error = 1.301181384860683e-13 relative error = 1.457388170378282e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.00576065718004454 y2[1] (numeric) = 0.005760657180717109 absolute error = 6.725687715092299e-13 relative error = 1.16752091035563e-08 % Correct digits = 9 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.704999999999922 y1[1] (analytic) = 0.9926110868511139 y1[1] (numeric) = 0.9926110868511779 absolute error = 6.405986852087153e-14 relative error = 6.453672477514867e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 2.729839136197677e-05 y2[1] (numeric) = 2.729839205933027e-05 absolute error = 6.973535044232405e-13 relative error = 2.554558967143267e-06 % Correct digits = 7 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.80499999999992 y1[1] (analytic) = 1.092478691995128 y1[1] (numeric) = 1.092478691995122 absolute error = 5.773159728050814e-15 relative error = 5.284459798028316e-13 % Correct digits = 14 h = 0.005 y2[1] (analytic) = 0.004285336290124616 y2[1] (numeric) = 0.004285336290840135 absolute error = 7.155187900509397e-13 relative error = 1.66969110848972e-08 % Correct digits = 9 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4.904999999999918 y1[1] (analytic) = 1.191422280618118 y1[1] (numeric) = 1.19142228061804 absolute error = 7.838174553853605e-14 relative error = 6.578838319010708e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 0.01849222596916822 y2[1] (numeric) = 0.01849222596989478 absolute error = 7.26564641784222e-13 relative error = 3.929027489690053e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 5.004999999999916 y1[1] (analytic) = 1.288453241088966 y1[1] (numeric) = 1.288453241088813 absolute error = 1.532107773982716e-13 relative error = 1.189106228401288e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.04250601688299314 y2[1] (numeric) = 0.04250601688372327 absolute error = 7.301312332508303e-13 relative error = 1.717712659976285e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 5.104999999999913 y1[1] (analytic) = 1.382602072124817 y1[1] (numeric) = 1.382602072124587 absolute error = 2.293720768875573e-13 relative error = 1.658988377871102e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.07608677117069236 y2[1] (numeric) = 0.07608677117141818 absolute error = 7.258221801365039e-13 relative error = 9.539400463034516e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 5.204999999999911 y1[1] (analytic) = 1.472928069727427 y1[1] (numeric) = 1.472928069727121 absolute error = 3.064215547965432e-13 relative error = 2.080356543502142e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.1188989610357448 y2[1] (numeric) = 0.1188989610364583 absolute error = 7.134987045631647e-13 relative error = 6.000882584236077e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 5.304999999999909 y1[1] (analytic) = 1.558528726386556 y1[1] (numeric) = 1.558528726386173 absolute error = 3.834710327055291e-13 relative error = 2.460468172406456e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.1705148212288472 y2[1] (numeric) = 0.17051482122954 absolute error = 6.928624340929446e-13 relative error = 4.063356071335623e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 5.404999999999907 y1[1] (analytic) = 1.638548748636682 y1[1] (numeric) = 1.638548748636223 absolute error = 4.591882429849647e-13 relative error = 2.802408188142233e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.2304186231368851 y2[1] (numeric) = 0.2304186231375489 absolute error = 6.638578575746124e-13 relative error = 2.88109462914477e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 5.504999999999905 y1[1] (analytic) = 1.712188602866583 y1[1] (numeric) = 1.71218860286605 absolute error = 5.333511410299252e-13 relative error = 3.115025646923342e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.2980118277727576 y2[1] (numeric) = 0.2980118277733841 absolute error = 6.264988527959758e-13 relative error = 2.102261703765995e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 5.604999999999903 y1[1] (analytic) = 1.778712503994894 y1[1] (numeric) = 1.778712503994291 absolute error = 6.032951915813101e-13 relative error = 3.391752125351011e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.3726190661790861 y2[1] (numeric) = 0.3726190661796669 absolute error = 5.808686864838819e-13 relative error = 1.558880742309381e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 5.704999999999901 y1[1] (analytic) = 1.837455767191419 y1[1] (numeric) = 1.837455767190749 absolute error = 6.701306176637445e-13 relative error = 3.647057140798823e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.4534948874915886 y2[1] (numeric) = 0.453494887492116 absolute error = 5.274669589994119e-13 relative error = 1.16311555774528e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 5.804999999999898 y1[1] (analytic) = 1.88783144918824 y1[1] (numeric) = 1.887831449187507 absolute error = 7.323031070427533e-13 relative error = 3.879070387124024e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.5398312072377027 y2[1] (numeric) = 0.539831207238169 absolute error = 4.662936703425657e-13 relative error = 8.637767955812966e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 5.904999999999896 y1[1] (analytic) = 1.92933621282283 y1[1] (numeric) = 1.929336212822041 absolute error = 7.889244812986362e-13 relative error = 4.089097981239638e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.6307653814495183 y2[1] (numeric) = 0.6307653814499162 absolute error = 3.979039320256561e-13 relative error = 6.308271565431517e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 6.004999999999894 y1[1] (analytic) = 1.961555356216604 y1[1] (numeric) = 1.961555356215765 absolute error = 8.386624728018433e-13 relative error = 4.275497350324251e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.7253888259171526 y2[1] (numeric) = 0.7253888259174758 absolute error = 3.231859224683831e-13 relative error = 4.455347407092462e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 6.104999999999892 y1[1] (analytic) = 1.984166956339004 y1[1] (numeric) = 1.984166956338123 absolute error = 8.810729923425242e-13 relative error = 4.440518422745011e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.8227560944618372 y2[1] (numeric) = 0.8227560944620791 absolute error = 2.419175970658216e-13 relative error = 2.940331875925627e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 6.20499999999989 y1[1] (analytic) = 1.996945085556008 y1[1] (numeric) = 1.996945085555092 absolute error = 9.157119507108291e-13 relative error = 4.585564006412665e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.9218943255216134 y2[1] (numeric) = 0.921894325521769 absolute error = 1.555422457499844e-13 relative error = 1.687202550704254e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 6.304999999999888 y1[1] (analytic) = 1.999762069024368 y1[1] (numeric) = 1.999762069023426 absolute error = 9.423573033018329e-13 relative error = 4.712347123183432e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.021812962662474 y2[1] (numeric) = 1.021812962662539 absolute error = 6.439293542825908e-14 relative error = 6.301831918482853e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 6.404999999999886 y1[1] (analytic) = 1.992589760376439 y1[1] (numeric) = 1.99258976037548 absolute error = 9.590106486712102e-13 relative error = 4.812885560999944e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.121513651890819 y2[1] (numeric) = 1.121513651890788 absolute error = 3.019806626980426e-14 relative error = 2.692616912767112e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 6.504999999999884 y1[1] (analytic) = 1.975499822949381 y1[1] (numeric) = 1.975499822948415 absolute error = 9.661160760288112e-13 relative error = 4.890489307087963e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.220000216876543 y2[1] (numeric) = 1.220000216876415 absolute error = 1.27675647831893e-13 relative error = 1.046521517502427e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 6.604999999999881 y1[1] (analytic) = 1.948663013748783 y1[1] (numeric) = 1.948663013747819 absolute error = 9.641176745844859e-13 relative error = 4.947585435666187e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.31628861241764 y2[1] (numeric) = 1.316288612417413 absolute error = 2.264854970235319e-13 relative error = 1.720637061560108e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 6.704999999999879 y1[1] (analytic) = 1.912347477301108 y1[1] (numeric) = 1.912347477300157 absolute error = 9.512390874988341e-13 relative error = 4.974195844582157e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.409416756694575 y2[1] (numeric) = 1.409416756694248 absolute error = 3.266276138447211e-13 relative error = 2.317466514381043e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 6.804999999999877 y1[1] (analytic) = 1.86691606644222 y1[1] (numeric) = 1.866916066441292 absolute error = 9.279244039817058e-13 relative error = 4.970359517822622e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.498454144073804 y2[1] (numeric) = 1.498454144073378 absolute error = 4.265476860609851e-13 relative error = 2.846584847110117e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 6.904999999999875 y1[1] (analytic) = 1.812822716811793 y1[1] (numeric) = 1.812822716810899 absolute error = 8.941736240331011e-13 relative error = 4.932493485108582e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.582511142412482 y2[1] (numeric) = 1.582511142411958 absolute error = 5.242473122279989e-13 relative error = 3.312755899012518e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 7.004999999999873 y1[1] (analytic) = 1.750607911278452 y1[1] (numeric) = 1.750607911277602 absolute error = 8.504308368628699e-13 relative error = 4.857917249110387e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.660747881968758 y2[1] (numeric) = 1.660747881968138 absolute error = 6.201705815556124e-13 relative error = 3.734284946493035e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 7.104999999999871 y1[1] (analytic) = 1.680893279613604 y1[1] (numeric) = 1.680893279612808 absolute error = 7.953637748414621e-13 relative error = 4.731792223146355e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.732382647102613 y2[1] (numeric) = 1.732382647101901 absolute error = 7.116529587847253e-13 relative error = 4.107943242071579e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 7.204999999999869 y1[1] (analytic) = 1.604375387372251 y1[1] (numeric) = 1.604375387371521 absolute error = 7.30304705598428e-13 relative error = 4.551956551730503e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.796699686920135 y2[1] (numeric) = 1.796699686919337 absolute error = 7.984723993104126e-13 relative error = 4.444106074728254e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 7.304999999999866 y1[1] (analytic) = 1.521818776040216 y1[1] (numeric) = 1.52181877603956 absolute error = 6.565858967633176e-13 relative error = 4.314481507921455e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.853056366819855 y2[1] (numeric) = 1.853056366818975 absolute error = 8.79296635503124e-13 relative error = 4.74511542793563e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 7.404999999999864 y1[1] (analytic) = 1.434048323988342 y1[1] (numeric) = 1.434048323987768 absolute error = 5.74207348336131e-13 relative error = 4.004100410920314e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.900889589485255 y2[1] (numeric) = 1.900889589484302 absolute error = 9.532374889431594e-13 relative error = 5.014691511889905e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 7.504999999999862 y1[1] (analytic) = 1.341941004560477 y1[1] (numeric) = 1.341941004559995 absolute error = 4.827249711070181e-13 relative error = 3.597214553147393e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.939721421167024 y2[1] (numeric) = 1.939721421166005 absolute error = 1.019406781210819e-12 relative error = 5.255428795530327e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 7.60499999999986 y1[1] (analytic) = 1.246417123645712 y1[1] (numeric) = 1.246417123645329 absolute error = 3.839151219153791e-13 relative error = 3.080149611491578e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.969163867039096 y2[1] (numeric) = 1.969163867038019 absolute error = 1.076916333886402e-12 relative error = 5.468901557216217e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 7.704999999999858 y1[1] (analytic) = 1.148431124286151 y1[1] (numeric) = 1.148431124285873 absolute error = 2.784439345759893e-13 relative error = 2.424559285164499e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.988922747914694 y2[1] (numeric) = 1.98892274791357 absolute error = 1.124211834735434e-12 relative error = 5.652365512507335e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 7.804999999999856 y1[1] (analytic) = 1.048962050197529 y1[1] (numeric) = 1.048962050197362 absolute error = 1.669775429036235e-13 relative error = 1.591835880737346e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.998800639587528 y2[1] (numeric) = 1.998800639586366 absolute error = 1.161293283757914e-12 relative error = 5.809950531122294e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 7.904999999999854 y1[1] (analytic) = 0.9490037634880352 y1[1] (numeric) = 0.9490037634879841 absolute error = 5.10702591327572e-14 relative error = 5.381460126675365e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.998698845429199 y2[1] (numeric) = 1.998698845428012 absolute error = 1.187494547139067e-12 relative error = 5.941338035265966e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 8.004999999999852 y1[1] (analytic) = 0.8495550143166543 y1[1] (numeric) = 0.8495550143167226 absolute error = 6.838973831690964e-14 relative error = 8.050065877360446e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.98861838253329 y2[1] (numeric) = 1.988618382532088 absolute error = 1.201705401854269e-12 relative error = 6.042916088925135e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 8.104999999999867 y1[1] (analytic) = 0.7516094617117036 y1[1] (numeric) = 0.7516094617119111 absolute error = 2.075006833024418e-13 relative error = 2.76075134591684e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.968659971552893 y2[1] (numeric) = 1.968659971551693 absolute error = 1.199262911200094e-12 relative error = 6.091772721188146e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 8.204999999999883 y1[1] (analytic) = 0.6561457452583349 y1[1] (numeric) = 0.6561457452586812 absolute error = 3.462785613805863e-13 relative error = 5.277464098227917e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.939023030333151 y2[1] (numeric) = 1.93902303033197 absolute error = 1.181277298201167e-12 relative error = 6.092126187888582e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 8.304999999999898 y1[1] (analytic) = 0.5641177068552412 y1[1] (numeric) = 0.5641177068557248 absolute error = 4.836131495267182e-13 relative error = 8.572912065155554e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.900003681394063 y2[1] (numeric) = 1.900003681392915 absolute error = 1.148192652067337e-12 relative error = 6.043107512428025e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 8.404999999999914 y1[1] (analytic) = 0.4764448602417215 y1[1] (numeric) = 0.476444860242339 absolute error = 6.175060462965121e-13 relative error = 1.296070328019121e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 1.851991793172146 y2[1] (numeric) = 1.851991793171048 absolute error = 1.09845466056413e-12 relative error = 5.931206955742844e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 8.50499999999993 y1[1] (analytic) = 0.3940032035203484 y1[1] (numeric) = 0.3940032035210946 absolute error = 7.461808948505677e-13 relative error = 1.893844740813208e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 1.795467084583894 y2[1] (numeric) = 1.79546708458286 absolute error = 1.033395591321096e-12 relative error = 5.755580819018963e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 8.604999999999945 y1[1] (analytic) = 0.3176164664734936 y1[1] (numeric) = 0.3176164664743614 absolute error = 8.677503160470224e-13 relative error = 2.732069674099972e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 1.730994331832935 y2[1] (numeric) = 1.730994331831982 absolute error = 9.534595335480844e-13 relative error = 5.508160922390048e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 8.704999999999961 y1[1] (analytic) = 0.2480478801276313 y1[1] (numeric) = 0.248047880128612 absolute error = 9.806322420757851e-13 relative error = 3.953399003334387e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 1.659217725352899 y2[1] (numeric) = 1.659217725352039 absolute error = 8.599787548746463e-13 relative error = 5.183037414162973e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 8.804999999999977 y1[1] (analytic) = 0.1859925508012124 y1[1] (numeric) = 0.1859925508022957 absolute error = 1.083327871853612e-12 relative error = 5.824576668188532e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 1.580854433269544 y2[1] (numeric) = 1.58085443326879 absolute error = 7.536193891155563e-13 relative error = 4.767164978984882e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 8.899999999999991 y1[1] (analytic) = 0.1345647907588922 y1[1] (numeric) = 0.1345647907600624 absolute error = 1.170175067954915e-12 relative error = 8.69599738055988e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 1.501020856457892 y2[1] (numeric) = 1.50102085645725 absolute error = 6.419309528382655e-13 relative error = 4.276629135940813e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 9.000000000000007 y1[1] (analytic) = 0.08886973811532008 y1[1] (numeric) = 0.08886973811656897 absolute error = 1.248889880400839e-12 relative error = 1.405303882836069e-09 % Correct digits = 10 h = 0.005 y2[1] (analytic) = 1.41211848524175 y2[1] (numeric) = 1.412118485241236 absolute error = 5.138112157965224e-13 relative error = 3.638584305541186e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 9.100000000000023 y1[1] (analytic) = 0.05227839786888072 y1[1] (numeric) = 0.05227839787019416 absolute error = 1.313435471494984e-12 relative error = 2.512386616723043e-09 % Correct digits = 10 h = 0.005 y2[1] (analytic) = 1.31909836234933 y2[1] (numeric) = 1.319098362348954 absolute error = 3.75921516138078e-13 relative error = 2.849836880007623e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 9.200000000000038 y1[1] (analytic) = 0.02515637859582771 y1[1] (numeric) = 0.02515637859719052 absolute error = 1.362812640515187e-12 relative error = 5.41736416998119e-09 % Correct digits = 10 h = 0.005 y2[1] (analytic) = 1.22288991410021 y2[1] (numeric) = 1.222889914099978 absolute error = 2.311484337269576e-13 relative error = 1.890181863974521e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 9.300000000000054 y1[1] (analytic) = 0.007774674547389872 y1[1] (numeric) = 0.007774674548786002 absolute error = 1.396129739594798e-12 relative error = 1.795740427570064e-08 % Correct digits = 9 h = 0.005 y2[1] (analytic) = 1.124454423507009 y2[1] (numeric) = 1.124454423506929 absolute error = 7.971401316808624e-14 relative error = 7.089127980791778e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 9.40000000000007 y1[1] (analytic) = 0.0003069579647918026 y1[1] (numeric) = 0.0003069579662044884 absolute error = 1.412685832029303e-12 relative error = 4.602212661226992e-07 % Correct digits = 8 h = 0.005 y2[1] (analytic) = 1.024775425453289 y2[1] (numeric) = 1.024775425453364 absolute error = 7.571721027943568e-14 relative error = 7.388663740247646e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 9.500000000000085 y1[1] (analytic) = 0.002827843803627935 y1[1] (numeric) = 0.002827843805039917 absolute error = 1.411981642718274e-12 relative error = 4.99313873314642e-08 % Correct digits = 9 h = 0.005 y2[1] (analytic) = 0.9248488795381057 y2[1] (numeric) = 0.9248488795383393 absolute error = 2.335909243811329e-13 relative error = 2.525719926241296e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 9.600000000000101 y1[1] (analytic) = 0.01531214420589068 y1[1] (numeric) = 0.01531214420728442 absolute error = 1.39373582119795e-12 relative error = 9.10215971360674e-09 % Correct digits = 10 h = 0.005 y2[1] (analytic) = 0.8256732187769207 y2[1] (numeric) = 0.8256732187773127 absolute error = 3.920197499951428e-13 relative error = 4.747880167118006e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 9.700000000000117 y1[1] (analytic) = 0.03763512016872163 y1[1] (numeric) = 0.03763512017007949 absolute error = 1.357851331373894e-12 relative error = 3.607936749734089e-09 % Correct digits = 10 h = 0.005 y2[1] (analytic) = 0.7282393735889447 y2[1] (numeric) = 0.7282393735894936 absolute error = 5.488942633746774e-13 relative error = 7.537278033589285e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 9.800000000000132 y1[1] (analytic) = 0.06957372789529491 y1[1] (numeric) = 0.06957372789659939 absolute error = 1.304484298358943e-12 relative error = 1.87496679827496e-09 % Correct digits = 10 h = 0.005 y2[1] (analytic) = 0.6335208707479493 y2[1] (numeric) = 0.6335208707486515 absolute error = 7.022160630754115e-13 relative error = 1.108433984576324e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 9.900000000000148 y1[1] (analytic) = 0.1108088473747066 y1[1] (numeric) = 0.1108088473759406 absolute error = 1.233999014083054e-12 relative error = 1.113628598545218e-09 % Correct digits = 10 h = 0.005 y2[1] (analytic) = 0.5424641062245475 y2[1] (numeric) = 0.5424641062253976 absolute error = 8.500977699554824e-13 relative error = 1.567104182932968e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 10.00000000000016 y1[1] (analytic) = 0.1609284709236365 y1[1] (numeric) = 0.1609284709247834 absolute error = 1.146915895589018e-12 relative error = 7.126867539388048e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 0.4559788891104931 y2[1] (numeric) = 0.4559788891114839 absolute error = 9.90818538326721e-13 relative error = 2.172948270170081e-10 % Correct digits = 11 h = 0.005 Finished! diff ( y1 , x , 1 ) = m1 * y2 + 1.0; diff ( y2 , x , 1 ) = y1 - 1.0; Iterations = 1980 Total Elapsed Time = 7 Minutes 26 Seconds Elapsed Time(since restart) = 7 Minutes 26 Seconds Time to Timeout = 2 Minutes 34 Seconds Percent Done = 100.1 %