##############ECHO OF PROBLEM################# ##############temp/mtest6_revpostode.ode################# diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1; diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; ! /* BEGIN FIRST INPUT BLOCK */ Digits = 32; max_terms = 30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ /* # */ /* # was complicatedrev.ode */ /* # */ t_start = 0.5; t_end = 5.0; array_x1_init[0 + 1] = exact_soln_x1(t_start); array_x1_init[1 + 1] = exact_soln_x1p(t_start); array_x2_init[0 + 1] = exact_soln_x2(t_start); array_x2_init[1 + 1] = exact_soln_x2p(t_start); glob_h = 0.00001 ; glob_look_poles = true; glob_max_iter = 10; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_h = 0.00001 ; glob_look_poles = true; glob_max_iter = 100; glob_max_minutes = 1; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_x1 (double t) { double c1,c2,c3; c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return(1.0 + 2.0 * c1 + 6.0 * c3 * exp(-t)); } double exact_soln_x1p (double t) { double c1,c2,c3; c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return( - 6.0 * c3 * exp(-t)); } double exact_soln_x2 (double t) { double c1,c2,c3; c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return(1.0 + c1 + c2 * exp(2.0 * t) + c3 * exp(-t)); } double exact_soln_x2p (double t) { double c1,c2,c3; c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return( 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion t[1] = 0.5 x2[1] (analytic) = 2.000725615563606 x2[1] (numeric) = 2.000725615563606 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 x1[1] (analytic) = 3.001091755187483 x1[1] (numeric) = 3.001091755187483 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 t[1] = 0.5 x2[1] (analytic) = 2.000725615563606 x2[1] (numeric) = 2.000725615563606 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 x1[1] (analytic) = 3.001091755187483 x1[1] (numeric) = 3.001091755187483 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50001 x2[1] (analytic) = 2.000725624617259 x2[1] (numeric) = 2.000725624617141 absolute error = 1.176836406102666e-13 relative error = 5.882047951116716e-12 % Correct digits = 13 h = 1e-05 x1[1] (analytic) = 3.001091744269985 x1[1] (numeric) = 3.001091744269931 absolute error = 5.417888360170764e-14 relative error = 1.805305809299297e-12 % Correct digits = 13 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5000199999999999 x2[1] (analytic) = 2.000725633671148 x2[1] (numeric) = 2.000725633670676 absolute error = 4.711786516509164e-13 relative error = 2.355038810525694e-11 % Correct digits = 12 h = 1e-05 x1[1] (analytic) = 3.001091733352597 x1[1] (numeric) = 3.001091733352379 absolute error = 2.180478020363807e-13 relative error = 7.265616029430526e-12 % Correct digits = 13 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5000299999999999 x2[1] (analytic) = 2.000725642725272 x2[1] (numeric) = 2.000725642724212 absolute error = 1.060040943912099e-12 relative error = 5.298282389524301e-11 % Correct digits = 12 h = 1e-05 x1[1] (analytic) = 3.001091722435318 x1[1] (numeric) = 3.001091722434828 absolute error = 4.907185768843192e-13 relative error = 1.635133552286473e-11 % Correct digits = 12 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5000399999999998 x2[1] (analytic) = 2.000725651779632 x2[1] (numeric) = 2.000725651777747 absolute error = 1.885158695813516e-12 relative error = 9.422374797547478e-11 % Correct digits = 12 h = 1e-05 x1[1] (analytic) = 3.001091711518149 x1[1] (numeric) = 3.001091711517276 absolute error = 8.72635297355373e-13 relative error = 2.907726191792843e-11 % Correct digits = 12 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5000499999999998 x2[1] (analytic) = 2.000725660834228 x2[1] (numeric) = 2.000725660831282 absolute error = 2.945643728935465e-12 relative error = 1.472287673716966e-10 % Correct digits = 11 h = 1e-05 x1[1] (analytic) = 3.001091700601088 x1[1] (numeric) = 3.001091700599724 absolute error = 1.363797963449542e-12 relative error = 4.544339525434652e-11 % Correct digits = 12 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5000599999999997 x2[1] (analytic) = 2.00072566988906 x2[1] (numeric) = 2.000725669884817 absolute error = 4.242384221697648e-12 relative error = 2.120422747378899e-10 % Correct digits = 11 h = 1e-05 x1[1] (analytic) = 3.001091689684137 x1[1] (numeric) = 3.001091689682172 absolute error = 1.964206575166827e-12 relative error = 6.544973557184315e-11 % Correct digits = 12 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5000699999999997 x2[1] (analytic) = 2.000725678944127 x2[1] (numeric) = 2.000725678938353 absolute error = 5.774047906470514e-12 relative error = 2.885976806934242e-10 % Correct digits = 11 h = 1e-05 x1[1] (analytic) = 3.001091678767295 x1[1] (numeric) = 3.001091678764621 absolute error = 2.673861132507227e-12 relative error = 8.909628291014161e-11 % Correct digits = 12 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5000799999999996 x2[1] (analytic) = 2.00072568799943 x2[1] (numeric) = 2.000725687991888 absolute error = 7.541967050883613e-12 relative error = 3.769615742988232e-10 % Correct digits = 11 h = 1e-05 x1[1] (analytic) = 3.001091667850561 x1[1] (numeric) = 3.001091667847069 absolute error = 3.492317546260892e-12 relative error = 1.163682397199868e-10 % Correct digits = 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5000899999999996 x2[1] (analytic) = 2.000725697054968 x2[1] (numeric) = 2.000725697045423 absolute error = 9.544809387307396e-12 relative error = 4.770673661740428e-10 % Correct digits = 11 h = 1e-05 x1[1] (analytic) = 3.001091656933937 x1[1] (numeric) = 3.001091656929517 absolute error = 4.420019905637673e-12 relative error = 1.472804036299705e-10 % Correct digits = 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5000999999999995 x2[1] (analytic) = 2.000725706110742 x2[1] (numeric) = 2.000725706098959 absolute error = 1.178390718337141e-11 relative error = 5.889816453789872e-10 % Correct digits = 11 h = 1e-05 x1[1] (analytic) = 3.001091646017422 x1[1] (numeric) = 3.001091646011965 absolute error = 5.456968210637569e-12 relative error = 1.818327746798136e-10 % Correct digits = 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5001099999999995 x2[1] (analytic) = 2.000725715166753 x2[1] (numeric) = 2.000725715152494 absolute error = 1.425881634986581e-11 relative error = 7.126822153469145e-10 % Correct digits = 11 h = 1e-05 x1[1] (analytic) = 3.001091635101017 x1[1] (numeric) = 3.001091635094414 absolute error = 6.603162461260581e-12 relative error = 2.200253529092363e-10 % Correct digits = 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5001199999999995 x2[1] (analytic) = 2.000725724222998 x2[1] (numeric) = 2.000725724206029 absolute error = 1.696909279758074e-11 relative error = 8.481468795114763e-10 % Correct digits = 11 h = 1e-05 x1[1] (analytic) = 3.001091624184721 x1[1] (numeric) = 3.001091624176862 absolute error = 7.858602657506708e-12 relative error = 2.618581383579578e-10 % Correct digits = 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5001299999999994 x2[1] (analytic) = 2.000725733279479 x2[1] (numeric) = 2.000725733259564 absolute error = 1.991518061572606e-11 relative error = 9.953978341190318e-10 % Correct digits = 11 h = 1e-05 x1[1] (analytic) = 3.001091613268533 x1[1] (numeric) = 3.00109161325931 absolute error = 9.22328879937595e-12 relative error = 3.073311310656968e-10 % Correct digits = 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5001399999999994 x2[1] (analytic) = 2.000725742336197 x2[1] (numeric) = 2.0007257423131 absolute error = 2.309707980430176e-11 relative error = 1.154435079009474e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091602352455 x1[1] (numeric) = 3.001091602341758 absolute error = 1.069677679765846e-11 relative error = 3.564295334828705e-10 % Correct digits = 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5001499999999993 x2[1] (analytic) = 2.00072575139315 x2[1] (numeric) = 2.000725751366635 absolute error = 2.651479036330784e-11 relative error = 1.325258614022687e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091591436486 x1[1] (numeric) = 3.001091591424207 absolute error = 1.227951074156408e-11 relative error = 4.091681432383887e-10 % Correct digits = 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5001599999999993 x2[1] (analytic) = 2.000725760450338 x2[1] (numeric) = 2.00072576042017 absolute error = 3.01683122927443e-11 relative error = 1.507868438998546e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091580520626 x1[1] (numeric) = 3.001091580506655 absolute error = 1.397149063109282e-11 relative error = 4.655469603719677e-10 % Correct digits = 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5001699999999992 x2[1] (analytic) = 2.000725769507762 x2[1] (numeric) = 2.000725769473705 absolute error = 3.40572015034013e-11 relative error = 1.702242357371164e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091569604876 x1[1] (numeric) = 3.001091569589103 absolute error = 1.577271646624467e-11 relative error = 5.255659849233228e-10 % Correct digits = 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5001799999999992 x2[1] (analytic) = 2.000725778565422 x2[1] (numeric) = 2.000725778527241 absolute error = 3.818190208448868e-11 relative error = 1.908402565386357e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091558689234 x1[1] (numeric) = 3.001091558671551 absolute error = 1.768274415780979e-11 relative error = 5.892104193426529e-10 % Correct digits = 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5001899999999991 x2[1] (analytic) = 2.000725787623318 x2[1] (numeric) = 2.000725787580776 absolute error = 4.254241403600645e-11 relative error = 2.126349062883975e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091547773702 x1[1] (numeric) = 3.001091547754 absolute error = 1.970246188420788e-11 relative error = 6.565098588486493e-10 % Correct digits = 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5001999999999991 x2[1] (analytic) = 2.000725796681449 x2[1] (numeric) = 2.000725796634311 absolute error = 4.713829326874475e-11 relative error = 2.356059653298407e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091536858279 x1[1] (numeric) = 3.001091536836448 absolute error = 2.183098146701923e-11 relative error = 7.2743470830194e-10 % Correct digits = 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.500209999999999 x2[1] (analytic) = 2.000725805739817 x2[1] (numeric) = 2.000725805687846 absolute error = 5.197042796112328e-11 relative error = 2.597578729280495e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091525942965 x1[1] (numeric) = 3.001091525918896 absolute error = 2.406874699545369e-11 relative error = 8.019997653317527e-10 % Correct digits = 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.500219999999999 x2[1] (analytic) = 2.000725814798419 x2[1] (numeric) = 2.000725814741382 absolute error = 5.703792993472234e-11 relative error = 2.850861897859259e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.00109151502776 x1[1] (numeric) = 3.001091515001344 absolute error = 2.641575846951127e-11 relative error = 8.802050299777989e-10 % Correct digits = 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.500229999999999 x2[1] (analytic) = 2.000725823857259 x2[1] (numeric) = 2.000725823794917 absolute error = 6.234168736796164e-11 relative error = 3.115953551685121e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091504112664 x1[1] (numeric) = 3.001091504083793 absolute error = 2.887157179998212e-11 relative error = 9.620357046900045e-10 % Correct digits = 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5002399999999989 x2[1] (analytic) = 2.000725832916333 x2[1] (numeric) = 2.000725832848452 absolute error = 6.788081208242147e-11 relative error = 3.392809297787486e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091493197678 x1[1] (numeric) = 3.001091493166241 absolute error = 3.143707516528593e-11 relative error = 1.047521384687595e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5002499999999989 x2[1] (analytic) = 2.000725841975643 x2[1] (numeric) = 2.000725841901987 absolute error = 7.365574816731169e-11 relative error = 3.681451332411409e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091482282801 x1[1] (numeric) = 3.001091482248689 absolute error = 3.411138038700301e-11 relative error = 1.136632474830656e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5002599999999988 x2[1] (analytic) = 2.000725851035189 x2[1] (numeric) = 2.000725850955523 absolute error = 7.966649562263228e-11 relative error = 3.98187965539668e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091471368032 x1[1] (numeric) = 3.001091471331137 absolute error = 3.68949315543432e-11 relative error = 1.22938377274868e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5002699999999988 x2[1] (analytic) = 2.00072586009497 x2[1] (numeric) = 2.000725860009058 absolute error = 8.591261035917341e-11 relative error = 4.294072070178336e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091460453373 x1[1] (numeric) = 3.001091460413586 absolute error = 3.978728457809666e-11 relative error = 1.325760480891376e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5002799999999987 x2[1] (analytic) = 2.000725869154989 x2[1] (numeric) = 2.000725869062593 absolute error = 9.239542464456463e-11 relative error = 4.618095165810399e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091449538823 x1[1] (numeric) = 3.001091449496034 absolute error = 4.278932763668308e-11 relative error = 1.425792194478396e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5002899999999987 x2[1] (analytic) = 2.000725878215242 x2[1] (numeric) = 2.000725878116128 absolute error = 9.911316212196652e-11 relative error = 4.953860156513843e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091438624382 x1[1] (numeric) = 3.001091438578482 absolute error = 4.590017255168277e-11 relative error = 1.529449318369391e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5002999999999986 x2[1] (analytic) = 2.00072588727573 x2[1] (numeric) = 2.000725887169664 absolute error = 1.060667109697988e-10 relative error = 5.301411434937924e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091427710051 x1[1] (numeric) = 3.00109142766093 absolute error = 4.912026341230558e-11 relative error = 1.636746650194068e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5003099999999986 x2[1] (analytic) = 2.000725896336455 x2[1] (numeric) = 2.000725896223199 absolute error = 1.132565152772713e-10 relative error = 5.66077119732674e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091416795828 x1[1] (numeric) = 3.001091416743379 absolute error = 5.24496002185515e-11 relative error = 1.74768418999213e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5003199999999985 x2[1] (analytic) = 2.000725905397416 x2[1] (numeric) = 2.000725905276734 absolute error = 1.206821309551742e-10 relative error = 6.031917247115486e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091405881715 x1[1] (numeric) = 3.001091405825827 absolute error = 5.588773888121068e-11 relative error = 1.862247140213011e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5003299999999985 x2[1] (analytic) = 2.000725914458612 x2[1] (numeric) = 2.000725914330269 absolute error = 1.283431139142976e-10 relative error = 6.414827387739751e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.00109139496771 x1[1] (numeric) = 3.001091394908275 absolute error = 5.943512348949298e-11 relative error = 1.980450298486577e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5003399999999985 x2[1] (analytic) = 2.000725923520045 x2[1] (numeric) = 2.000725923383805 absolute error = 1.362403523330613e-10 relative error = 6.809546011847651e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091384053815 x1[1] (numeric) = 3.001091383990723 absolute error = 6.30917540433984e-11 relative error = 2.102293664852528e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5003499999999984 x2[1] (analytic) = 2.000725932581713 x2[1] (numeric) = 2.00072593243734 absolute error = 1.443729580330455e-10 relative error = 7.216028726470715e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091373140029 x1[1] (numeric) = 3.001091373073172 absolute error = 6.685763054292693e-11 relative error = 2.227777239350566e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5003599999999984 x2[1] (analytic) = 2.000725941643617 x2[1] (numeric) = 2.000725941490875 absolute error = 1.527418191926699e-10 relative error = 7.63431992425664e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091362226353 x1[1] (numeric) = 3.00109136215562 absolute error = 7.073275298807857e-11 relative error = 2.356901022020391e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5003699999999983 x2[1] (analytic) = 2.000725950705756 x2[1] (numeric) = 2.00072595054441 absolute error = 1.613460476335149e-10 relative error = 8.064375212237341e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091351312785 x1[1] (numeric) = 3.001091351238068 absolute error = 7.471667728964348e-11 relative error = 2.489650215311164e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5003799999999983 x2[1] (analytic) = 2.000725959768132 x2[1] (numeric) = 2.000725959597946 absolute error = 1.701860874447902e-10 relative error = 8.506216786656453e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091340399326 x1[1] (numeric) = 3.001091340320516 absolute error = 7.880984753683151e-11 relative error = 2.626039616853016e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5003899999999982 x2[1] (analytic) = 2.000725968830743 x2[1] (numeric) = 2.000725968651481 absolute error = 1.792623827157058e-10 relative error = 8.959866843757202e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091329485977 x1[1] (numeric) = 3.001091329402965 absolute error = 8.301226372964265e-11 relative error = 2.766069226685643e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5003999999999982 x2[1] (analytic) = 2.00072597789359 x2[1] (numeric) = 2.000725977705016 absolute error = 1.885740452678419e-10 relative error = 9.425280990572082e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091318572736 x1[1] (numeric) = 3.001091318485413 absolute error = 8.732348177886706e-11 relative error = 2.909724247258044e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5004099999999981 x2[1] (analytic) = 2.000725986956673 x2[1] (numeric) = 2.000725986758551 absolute error = 1.981215191904084e-10 relative error = 9.9024814233444e-09 % Correct digits = 10 h = 1e-05 x1[1] (analytic) = 3.001091307659606 x1[1] (numeric) = 3.001091307567861 absolute error = 9.174438986292444e-11 relative error = 3.057034273791259e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5004199999999981 x2[1] (analytic) = 2.000725996019992 x2[1] (numeric) = 2.000725995812087 absolute error = 2.079052485726152e-10 relative error = 1.039149033831706e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091296746583 x1[1] (numeric) = 3.001091296650309 absolute error = 9.627409980339507e-11 relative error = 3.207969711143533e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.500429999999998 x2[1] (analytic) = 2.000726005083546 x2[1] (numeric) = 2.000726004865622 absolute error = 2.179243452360424e-10 relative error = 1.089226334252312e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.00109128583367 x1[1] (numeric) = 3.001091285732758 absolute error = 1.00912611600279e-10 relative error = 3.362530559354397e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.500439999999998 x2[1] (analytic) = 2.000726014147337 x2[1] (numeric) = 2.000726013919157 absolute error = 2.281796973591099e-10 relative error = 1.140484482860862e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091274920867 x1[1] (numeric) = 3.001091274815206 absolute error = 1.056608134319958e-10 relative error = 3.520746413645214e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.500449999999998 x2[1] (analytic) = 2.000726023211363 x2[1] (numeric) = 2.000726022972692 absolute error = 2.386708608526078e-10 relative error = 1.192921260000994e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091264008172 x1[1] (numeric) = 3.001091263897654 absolute error = 1.10517817120126e-10 relative error = 3.682587678873902e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5004599999999979 x2[1] (analytic) = 2.000726032275626 x2[1] (numeric) = 2.000726032026228 absolute error = 2.493978357165361e-10 relative error = 1.246536665656672e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091253095586 x1[1] (numeric) = 3.001091252980102 absolute error = 1.154840667538792e-10 relative error = 3.848069152671014e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5004699999999979 x2[1] (analytic) = 2.000726041340123 x2[1] (numeric) = 2.000726041079763 absolute error = 2.603601778616849e-10 relative error = 1.301328480171582e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.00109124218311 x1[1] (numeric) = 3.001091242062551 absolute error = 1.205595623332556e-10 relative error = 4.01719083507624e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5004799999999978 x2[1] (analytic) = 2.000726050404857 x2[1] (numeric) = 2.000726050133298 absolute error = 2.715587754664739e-10 relative error = 1.357301142810244e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091231270743 x1[1] (numeric) = 3.001091231144999 absolute error = 1.257438597690452e-10 relative error = 4.189937928538144e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5004899999999978 x2[1] (analytic) = 2.000726059469827 x2[1] (numeric) = 2.000726059186833 absolute error = 2.829931844416933e-10 relative error = 1.414452433916334e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091220358485 x1[1] (numeric) = 3.001091220227447 absolute error = 1.31037403150458e-10 relative error = 4.366325230687436e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5004999999999977 x2[1] (analytic) = 2.000726068535032 x2[1] (numeric) = 2.000726068240369 absolute error = 2.946634047873431e-10 relative error = 1.472782353473812e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091209446336 x1[1] (numeric) = 3.001091209309895 absolute error = 1.364401924774938e-10 relative error = 4.546352741563806e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5005099999999977 x2[1] (analytic) = 2.000726077600474 x2[1] (numeric) = 2.000726077293904 absolute error = 3.065698805926331e-10 relative error = 1.532293121106868e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091198534296 x1[1] (numeric) = 3.001091198392344 absolute error = 1.419522277501528e-10 relative error = 4.730020461206941e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5005199999999976 x2[1] (analytic) = 2.000726086666151 x2[1] (numeric) = 2.000726086347439 absolute error = 3.187117236791437e-10 relative error = 1.592980297518984e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091187622365 x1[1] (numeric) = 3.001091187474792 absolute error = 1.475730648792251e-10 relative error = 4.917313592065186e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5005299999999976 x2[1] (analytic) = 2.000726095732064 x2[1] (numeric) = 2.000726095400974 absolute error = 3.310893781360846e-10 relative error = 1.654846102334359e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091176710543 x1[1] (numeric) = 3.00109117655724 absolute error = 1.533031479539204e-10 relative error = 5.108246931769463e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5005399999999975 x2[1] (analytic) = 2.000726104798213 x2[1] (numeric) = 2.00072610445451 absolute error = 3.437032880526658e-10 relative error = 1.717892755177154e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091165798831 x1[1] (numeric) = 3.001091165639688 absolute error = 1.591424769742389e-10 relative error = 5.30282048035946e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5005499999999975 x2[1] (analytic) = 2.000726113864598 x2[1] (numeric) = 2.000726113508045 absolute error = 3.565530093396774e-10 relative error = 1.7821180363911e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091154887227 x1[1] (numeric) = 3.001091154722137 absolute error = 1.650906078509706e-10 relative error = 5.501019440283355e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5005599999999975 x2[1] (analytic) = 2.000726122931219 x2[1] (numeric) = 2.00072612256158 absolute error = 3.696385419971193e-10 relative error = 1.847521945960151e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091143975733 x1[1] (numeric) = 3.001091143804585 absolute error = 1.711479846733255e-10 relative error = 5.702858609172231e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5005699999999974 x2[1] (analytic) = 2.000726131998075 x2[1] (numeric) = 2.000726131615115 absolute error = 3.829598860249916e-10 relative error = 1.91410448386826e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091133064348 x1[1] (numeric) = 3.001091132887033 absolute error = 1.773146074413035e-10 relative error = 5.908337987065772e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5005799999999974 x2[1] (analytic) = 2.000726141065168 x2[1] (numeric) = 2.000726140668651 absolute error = 3.965174855125042e-10 relative error = 1.981867869739544e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091122153072 x1[1] (numeric) = 3.001091121969481 absolute error = 1.835904761549045e-10 relative error = 6.11745757400366e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5005899999999973 x2[1] (analytic) = 2.000726150132496 x2[1] (numeric) = 2.000726149722186 absolute error = 4.103104522812373e-10 relative error = 2.050807664277617e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091111241905 x1[1] (numeric) = 3.00109111105193 absolute error = 1.899751467249189e-10 relative error = 6.330202572433857e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5005999999999973 x2[1] (analytic) = 2.000726159200061 x2[1] (numeric) = 2.000726158775721 absolute error = 4.243396745096106e-10 relative error = 2.120928306746746e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091100330847 x1[1] (numeric) = 3.001091100134378 absolute error = 1.964690632405564e-10 relative error = 6.546587779987657e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5006099999999972 x2[1] (analytic) = 2.000726168267861 x2[1] (numeric) = 2.000726167829256 absolute error = 4.386047081084143e-10 relative error = 2.19222757749072e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091089419898 x1[1] (numeric) = 3.001091089216826 absolute error = 2.030722257018169e-10 relative error = 6.766613196704742e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5006199999999972 x2[1] (analytic) = 2.000726177335897 x2[1] (numeric) = 2.000726176882792 absolute error = 4.531055530776484e-10 relative error = 2.264705476493486e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091078509059 x1[1] (numeric) = 3.001091078299274 absolute error = 2.097841900194908e-10 relative error = 6.990264025032906e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5006299999999971 x2[1] (analytic) = 2.00072618640417 x2[1] (numeric) = 2.000726185936327 absolute error = 4.678426535065228e-10 relative error = 2.338364223379106e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091067598328 x1[1] (numeric) = 3.001091067381723 absolute error = 2.166054002827877e-10 relative error = 7.217555062603606e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5006399999999971 x2[1] (analytic) = 2.000726195472677 x2[1] (numeric) = 2.000726194989862 absolute error = 4.828151212166176e-10 relative error = 2.413199378851293e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091056687707 x1[1] (numeric) = 3.001091056464171 absolute error = 2.235358564917078e-10 relative error = 7.448486309456519e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.500649999999997 x2[1] (analytic) = 2.000726204541421 x2[1] (numeric) = 2.000726204043398 absolute error = 4.980238443863527e-10 relative error = 2.489215382174208e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091045777194 x1[1] (numeric) = 3.001091045546619 absolute error = 2.305751145570412e-10 relative error = 7.683042968039279e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.500659999999997 x2[1] (analytic) = 2.000726213610402 x2[1] (numeric) = 2.000726213096933 absolute error = 5.13468823015728e-10 relative error = 2.566412233331767e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091034866791 x1[1] (numeric) = 3.001091034629067 absolute error = 2.377236185679976e-10 relative error = 7.921239835983497e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.500669999999997 x2[1] (analytic) = 2.000726222679617 x2[1] (numeric) = 2.000726222150468 absolute error = 5.291491689263239e-10 relative error = 2.64478549302774e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091023956497 x1[1] (numeric) = 3.001091023711516 absolute error = 2.449813685245772e-10 relative error = 8.163076913328851e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5006799999999969 x2[1] (analytic) = 2.000726231749069 x2[1] (numeric) = 2.000726231204003 absolute error = 5.4506577029656e-10 relative error = 2.724339600526226e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091013046312 x1[1] (numeric) = 3.001091012793964 absolute error = 2.5234792033757e-10 relative error = 8.408539402522808e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5006899999999969 x2[1] (analytic) = 2.000726240818757 x2[1] (numeric) = 2.000726240257539 absolute error = 5.612181830372265e-10 relative error = 2.805072336171086e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001091002136236 x1[1] (numeric) = 3.001091001876412 absolute error = 2.59823718096186e-10 relative error = 8.657642101197143e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5006999999999968 x2[1] (analytic) = 2.000726249888681 x2[1] (numeric) = 2.000726249311074 absolute error = 5.776068512375332e-10 relative error = 2.886985919586305e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001090991226269 x1[1] (numeric) = 3.00109099095886 absolute error = 2.674087618004251e-10 relative error = 8.910385009391526e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5007099999999968 x2[1] (analytic) = 2.00072625895884 x2[1] (numeric) = 2.000726258364609 absolute error = 5.942313308082703e-10 relative error = 2.970078131115762e-08 % Correct digits = 9 h = 1e-05 x1[1] (analytic) = 3.001090980316411 x1[1] (numeric) = 3.001090980041309 absolute error = 2.751026073610774e-10 relative error = 9.166753329553267e-09 % Correct digits = 10 h = 1e-05 Finished! Maximum Time Reached before Solution Completed! diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1; diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; Iterations = 71 Total Elapsed Time = 1 Minutes 1 Seconds Elapsed Time(since restart) = 1 Minutes 0 Seconds Expected Time Remaining = 4 Days 9 Hours 53 Minutes 9 Seconds Optimized Time Remaining = 4 Days 8 Hours 9 Minutes 0 Seconds Time to Timeout Unknown Percent Done = 0.016 %