##############ECHO OF PROBLEM################# ##############temp/div_lin_linpostode.ode################# diff ( y , x , 1 ) = (0.1 * x + 0.2) / (0.2 * x + 0.3); ! // BEGIN FIRST INPUT BLOCK Digits = 32; max_terms = 30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start = 0.1; x_end = 5.0 ; array_y_init[0 + 1] = exact_soln_y(x_start); glob_h = 0.05; glob_look_poles = true; glob_max_iter = 1000000; // 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_y (double x) { return(0.5 * x + 0.25 * ln(2.0 * x + 3.0)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 0.3407877024514202 y[1] (numeric) = 0.3407877024514202 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 0.2000000000000001 y[1] (analytic) = 0.405943857905529 y[1] (numeric) = 0.4059438579055061 absolute error = 2.292610545850948e-14 relative error = 5.647604961138451e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 0.3000000000000002 y[1] (analytic) = 0.4702334613655162 y[1] (numeric) = 0.4702334613654773 absolute error = 3.885780586188048e-14 relative error = 8.263513563888215e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 0.4000000000000002 y[1] (analytic) = 0.5337502666830851 y[1] (numeric) = 0.5337502666830349 absolute error = 5.018208071305708e-14 relative error = 9.401790283854369e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 0.5965735902799729 y[1] (numeric) = 0.5965735902799142 absolute error = 5.873079800267078e-14 relative error = 9.844686214672749e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 0.6000000000000004 y[1] (analytic) = 0.658771131322331 y[1] (numeric) = 0.6587711313222658 absolute error = 6.517009154549669e-14 relative error = 9.892675687637187e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 0.7000000000000005 y[1] (analytic) = 0.7204011352310542 y[1] (numeric) = 0.7204011352309846 absolute error = 6.961098364399732e-14 relative error = 9.662808710270979e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 0.8000000000000006 y[1] (analytic) = 0.7815140758737626 y[1] (numeric) = 0.7815140758736895 absolute error = 7.316369732279782e-14 relative error = 9.361788812440518e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 0.9000000000000007 y[1] (analytic) = 0.8421539794784617 y[1] (numeric) = 0.842153979478386 absolute error = 7.571721027943568e-14 relative error = 8.990898591529147e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.000000000000001 y[1] (analytic) = 0.9023594781085256 y[1] (numeric) = 0.9023594781084475 absolute error = 7.80486786311485e-14 relative error = 8.649399770782005e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 0.3437 Order of pole = 0.5095 Complex estimate of poles used Complex estimate of poles used x[1] = 1.104999999999998 y[1] (analytic) = 0.965144963941318 y[1] (numeric) = 0.9651449639412394 absolute error = 7.860379014346108e-14 relative error = 8.144247038545424e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.204999999999996 y[1] (analytic) = 1.024562273214595 y[1] (numeric) = 1.024562273214517 absolute error = 7.860379014346108e-14 relative error = 7.671938758474807e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 0.7905 Order of pole = 0.5427 Complex estimate of poles used x[1] = 1.304999999999994 y[1] (analytic) = 1.083637679883648 y[1] (numeric) = 1.083637679883569 absolute error = 7.838174553853605e-14 relative error = 7.233205986981927e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 1.404999999999992 y[1] (analytic) = 1.14239514271595 y[1] (numeric) = 1.142395142715872 absolute error = 7.793765632868599e-14 relative error = 6.82230284552818e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 3.945 Order of pole = 1.422 Complex estimate of poles used Complex estimate of poles used x[1] = 1.50499999999999 y[1] (analytic) = 1.200856187136773 y[1] (numeric) = 1.200856187136696 absolute error = 7.72715225139109e-14 relative error = 6.434702451602554e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.604999999999988 y[1] (analytic) = 1.25904022398634 y[1] (numeric) = 1.259040223986263 absolute error = 7.682743330406083e-14 relative error = 6.102063448045516e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.704999999999986 y[1] (analytic) = 1.316964817733136 y[1] (numeric) = 1.316964817733061 absolute error = 7.571721027943568e-14 relative error = 5.749372288453849e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.804999999999984 y[1] (analytic) = 1.374645913465889 y[1] (numeric) = 1.374645913465814 absolute error = 7.505107646466058e-14 relative error = 5.459666065964188e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.904999999999981 y[1] (analytic) = 1.432098030040345 y[1] (numeric) = 1.43209803004027 absolute error = 7.438494264988549e-14 relative error = 5.194123662595217e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 2.004999999999979 y[1] (analytic) = 1.489334425261613 y[1] (numeric) = 1.48933442526154 absolute error = 7.327471962526033e-14 relative error = 4.919964138503618e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 2.104999999999977 y[1] (analytic) = 1.546367237824201 y[1] (numeric) = 1.54636723782413 absolute error = 7.172040739078511e-14 relative error = 4.637993203457834e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 2.204999999999975 y[1] (analytic) = 1.603207609826985 y[1] (numeric) = 1.603207609826914 absolute error = 7.061018436615996e-14 relative error = 4.404306961453363e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 2.304999999999973 y[1] (analytic) = 1.659865792968383 y[1] (numeric) = 1.659865792968314 absolute error = 6.927791673660977e-14 relative error = 4.173705912254399e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 2.404999999999971 y[1] (analytic) = 1.716351240962882 y[1] (numeric) = 1.716351240962814 absolute error = 6.861178292183467e-14 relative error = 3.997537408680003e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 7.145 Order of pole = 2.174 Complex estimate of poles used Complex estimate of poles used x[1] = 2.504999999999969 y[1] (analytic) = 1.772672690270049 y[1] (numeric) = 1.772672690269982 absolute error = 6.727951529228449e-14 relative error = 3.795371568681137e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 2.604999999999967 y[1] (analytic) = 1.828838230866066 y[1] (numeric) = 1.828838230865999 absolute error = 6.616929226765933e-14 relative error = 3.618105262176424e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 2.704999999999965 y[1] (analytic) = 1.884855368496194 y[1] (numeric) = 1.88485536849613 absolute error = 6.483702463810914e-14 relative error = 3.439893889038205e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 2.804999999999962 y[1] (analytic) = 1.940731079609889 y[1] (numeric) = 1.940731079609825 absolute error = 6.372680161348399e-14 relative error = 3.283649253779862e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 2.90499999999996 y[1] (analytic) = 1.996471859987 y[1] (numeric) = 1.996471859986937 absolute error = 6.328271240363392e-14 relative error = 3.169727240936218e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 3.004999999999958 y[1] (analytic) = 2.052083767905038 y[1] (numeric) = 2.052083767904977 absolute error = 6.17284001691587e-14 relative error = 3.008083838223471e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 16.13 Order of pole = 6.91 Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 3.104999999999956 y[1] (analytic) = 2.107572462566779 y[1] (numeric) = 2.107572462566718 absolute error = 6.084022174945858e-14 relative error = 2.886744006674021e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 3.204999999999954 y[1] (analytic) = 2.162943238399297 y[1] (numeric) = 2.162943238399236 absolute error = 6.039613253960852e-14 relative error = 2.792312413353258e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 3.304999999999952 y[1] (analytic) = 2.218201055745523 y[1] (numeric) = 2.218201055745464 absolute error = 5.950795411990839e-14 relative error = 2.682712370268354e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 7.71 Order of pole = 1.787 Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 3.40499999999995 y[1] (analytic) = 2.27335056839429 y[1] (numeric) = 2.273350568394232 absolute error = 5.773159728050814e-14 relative error = 2.539493823923736e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 3.504999999999947 y[1] (analytic) = 2.328396148331754 y[1] (numeric) = 2.328396148331697 absolute error = 5.684341886080801e-14 relative error = 2.441312183991333e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 3.604999999999945 y[1] (analytic) = 2.383341908044113 y[1] (numeric) = 2.383341908044058 absolute error = 5.551115123125783e-14 relative error = 2.329130832798261e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 3.704999999999943 y[1] (analytic) = 2.438191720656688 y[1] (numeric) = 2.438191720656634 absolute error = 5.46229728115577e-14 relative error = 2.240306713733154e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 3.804999999999941 y[1] (analytic) = 2.492949238156441 y[1] (numeric) = 2.492949238156387 absolute error = 5.329070518200751e-14 relative error = 2.137657051589887e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.484 Order of pole = 0.6096 Complex estimate of poles used Complex estimate of poles used x[1] = 3.904999999999939 y[1] (analytic) = 2.547617907912746 y[1] (numeric) = 2.547617907912693 absolute error = 5.240252676230739e-14 relative error = 2.056922531418402e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 4.004999999999937 y[1] (analytic) = 2.602200987683613 y[1] (numeric) = 2.60220098768356 absolute error = 5.284661597215745e-14 relative error = 2.030842975707254e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 2.656701559270982 y[1] (numeric) = 2.65670155927093 absolute error = 5.151434834260726e-14 relative error = 1.93903406887536e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 4.204999999999933 y[1] (analytic) = 2.711122540968459 y[1] (numeric) = 2.71112254096841 absolute error = 4.973799150320701e-14 relative error = 1.834590312743287e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 4.30499999999993 y[1] (analytic) = 2.765466698927412 y[1] (numeric) = 2.765466698927364 absolute error = 4.840572387365683e-14 relative error = 1.750363650823603e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 4.404999999999928 y[1] (analytic) = 2.819736657552279 y[1] (numeric) = 2.819736657552232 absolute error = 4.707345624410664e-14 relative error = 1.669427395569967e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 4.504999999999926 y[1] (analytic) = 2.873934909022933 y[1] (numeric) = 2.873934909022888 absolute error = 4.485301019485632e-14 relative error = 1.560682883040842e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 4.604999999999924 y[1] (analytic) = 2.928063822030612 y[1] (numeric) = 2.928063822030569 absolute error = 4.307665335545607e-14 relative error = 1.471165110246211e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 3.159 Order of pole = 0.6339 Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 4.704999999999922 y[1] (analytic) = 2.982125649804087 y[1] (numeric) = 2.982125649804045 absolute error = 4.218847493575595e-14 relative error = 1.414711514202212e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 4.80499999999992 y[1] (analytic) = 3.036122537494164 y[1] (numeric) = 3.036122537494123 absolute error = 4.04121180963557e-14 relative error = 1.331043711091762e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 4.904999999999918 y[1] (analytic) = 3.090056528977116 y[1] (numeric) = 3.090056528977077 absolute error = 3.907985046680551e-14 relative error = 1.264696943254365e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 7.374 Order of pole = 1.163 Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 5.004999999999916 y[1] (analytic) = 3.143929573131058 y[1] (numeric) = 3.14392957313102 absolute error = 3.774758283725532e-14 relative error = 1.200649758819574e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = (0.1 * x + 0.2) / (0.2 * x + 0.3); Iterations = 981 Total Elapsed Time = 48 Seconds Elapsed Time(since restart) = 47 Seconds Time to Timeout = 9 Minutes 12 Seconds Percent Done = 100.2 %