##############ECHO OF PROBLEM################# ##############temp/mtest6postode.ode################# diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1; ! // BEGIN FIRST INPUT BLOCK Digits = 32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK // # // # was complicated.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(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(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 x1[1] (analytic) = 2.001091755187483 x1[1] (numeric) = 2.001091755187483 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 x2[1] (analytic) = 1.000725615563606 x2[1] (numeric) = 1.000725615563606 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 t[1] = 0.5 x1[1] (analytic) = 2.001091755187483 x1[1] (numeric) = 2.001091755187483 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 x2[1] (analytic) = 1.000725615563606 x2[1] (numeric) = 1.000725615563606 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50001 x1[1] (analytic) = 2.001091744269985 x1[1] (numeric) = 2.001091744269931 absolute error = 5.417888360170764e-14 relative error = 2.707466249703236e-12 % Correct digits = 13 h = 1e-05 x2[1] (analytic) = 1.000725624617259 x2[1] (numeric) = 1.000725624617141 absolute error = 1.179056852151916e-13 relative error = 1.178201919834783e-11 % Correct digits = 12 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5000199999999999 x1[1] (analytic) = 2.001091733352597 x1[1] (numeric) = 2.001091733352379 absolute error = 2.180478020363807e-13 relative error = 1.089644209718796e-11 % Correct digits = 12 h = 1e-05 x2[1] (analytic) = 1.000725633671148 x2[1] (numeric) = 1.000725633670676 absolute error = 4.716227408607665e-13 relative error = 4.712807636700833e-11 % Correct digits = 12 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5000299999999999 x1[1] (analytic) = 2.001091722435318 x1[1] (numeric) = 2.001091722434828 absolute error = 4.907185768843192e-13 relative error = 2.452254293906714e-11 % Correct digits = 12 h = 1e-05 x2[1] (analytic) = 1.000725642725272 x2[1] (numeric) = 1.000725642724211 absolute error = 1.0609291223318e-12 relative error = 1.060159825067114e-10 % Correct digits = 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5000399999999998 x1[1] (analytic) = 2.001091711518149 x1[1] (numeric) = 2.001091711517276 absolute error = 8.72635297355373e-13 relative error = 4.360796121100014e-11 % Correct digits = 12 h = 1e-05 x2[1] (analytic) = 1.000725651779632 x2[1] (numeric) = 1.000725651777747 absolute error = 1.885824829628291e-12 relative error = 1.884457369784266e-10 % Correct digits = 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5000499999999998 x1[1] (analytic) = 2.001091700601088 x1[1] (numeric) = 2.001091700599724 absolute error = 1.363797963449542e-12 relative error = 6.815269700233551e-11 % Correct digits = 12 h = 1e-05 x2[1] (analytic) = 1.000725660834228 x2[1] (numeric) = 1.000725660831282 absolute error = 2.94630986275024e-12 relative error = 2.944173391430903e-10 % Correct digits = 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5000599999999997 x1[1] (analytic) = 2.001091689684137 x1[1] (numeric) = 2.001091689682172 absolute error = 1.964206575166827e-12 relative error = 9.815675040241999e-11 % Correct digits = 12 h = 1e-05 x2[1] (analytic) = 1.00072566988906 x2[1] (numeric) = 1.000725669884817 absolute error = 4.242606266302573e-12 relative error = 4.239529767206739e-10 % Correct digits = 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5000699999999997 x1[1] (analytic) = 2.001091678767295 x1[1] (numeric) = 2.001091678764621 absolute error = 2.673861132507227e-12 relative error = 1.336201215005986e-10 % Correct digits = 11 h = 1e-05 x2[1] (analytic) = 1.000725678944127 x2[1] (numeric) = 1.000725678938352 absolute error = 5.774714040285289e-12 relative error = 5.770526490714451e-10 % Correct digits = 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5000799999999996 x1[1] (analytic) = 2.001091667850561 x1[1] (numeric) = 2.001091667847069 absolute error = 3.492317546260892e-12 relative error = 1.74520618039058e-10 % Correct digits = 11 h = 1e-05 x2[1] (analytic) = 1.00072568799943 x2[1] (numeric) = 1.000725687991888 absolute error = 7.542189095488538e-12 relative error = 7.536719788383044e-10 % Correct digits = 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5000899999999996 x1[1] (analytic) = 2.001091656933937 x1[1] (numeric) = 2.001091656929517 absolute error = 4.420019905637673e-12 relative error = 2.208804324540539e-10 % Correct digits = 11 h = 1e-05 x2[1] (analytic) = 1.000725697054968 x2[1] (numeric) = 1.000725697045423 absolute error = 9.545475521122171e-12 relative error = 9.538553420995897e-10 % Correct digits = 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5000999999999995 x1[1] (analytic) = 2.001091646017422 x1[1] (numeric) = 2.001091646011965 absolute error = 5.456968210637569e-12 relative error = 2.726995648349261e-10 % Correct digits = 11 h = 1e-05 x2[1] (analytic) = 1.000725706110743 x2[1] (numeric) = 1.000725706098958 absolute error = 1.178457331718619e-11 relative error = 1.177602738215468e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5001099999999995 x1[1] (analytic) = 2.001091635101017 x1[1] (numeric) = 2.001091635094414 absolute error = 6.603162461260581e-12 relative error = 3.299780152710122e-10 % Correct digits = 11 h = 1e-05 x2[1] (analytic) = 1.000725715166752 x2[1] (numeric) = 1.000725715152493 absolute error = 1.425903839447074e-11 relative error = 1.424869789829947e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5001199999999995 x1[1] (analytic) = 2.001091624184721 x1[1] (numeric) = 2.001091624176862 absolute error = 7.858602657506708e-12 relative error = 3.927157838516484e-10 % Correct digits = 11 h = 1e-05 x2[1] (analytic) = 1.000725724222998 x2[1] (numeric) = 1.000725724206029 absolute error = 1.696975893139552e-11 relative error = 1.695745249735784e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5001299999999994 x1[1] (analytic) = 2.001091613268533 x1[1] (numeric) = 2.00109161325931 absolute error = 9.22328879937595e-12 relative error = 4.60912870666169e-10 % Correct digits = 11 h = 1e-05 x2[1] (analytic) = 1.00072573327948 x2[1] (numeric) = 1.000725733259564 absolute error = 1.991584674954083e-11 relative error = 1.990140363861193e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5001399999999994 x1[1] (analytic) = 2.001091602352455 x1[1] (numeric) = 2.001091602341758 absolute error = 1.069677679765846e-11 relative error = 5.345470834560236e-10 % Correct digits = 11 h = 1e-05 x2[1] (analytic) = 1.000725742336197 x2[1] (numeric) = 1.000725742313099 absolute error = 2.309774593811653e-11 relative error = 2.308099508282338e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5001499999999993 x1[1] (analytic) = 2.001091591436486 x1[1] (numeric) = 2.001091591424207 absolute error = 1.227951074156408e-11 relative error = 6.136406146581835e-10 % Correct digits = 11 h = 1e-05 x2[1] (analytic) = 1.00072575139315 x2[1] (numeric) = 1.000725751366634 absolute error = 2.651523445251769e-11 relative error = 2.649600494001957e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5001599999999993 x1[1] (analytic) = 2.001091580520626 x1[1] (numeric) = 2.001091580506655 absolute error = 1.397149063109282e-11 relative error = 6.981934643619779e-10 % Correct digits = 11 h = 1e-05 x2[1] (analytic) = 1.000725760450338 x2[1] (numeric) = 1.00072576042017 absolute error = 3.016853433734923e-11 relative error = 3.014665508737683e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5001699999999992 x1[1] (analytic) = 2.001091569604876 x1[1] (numeric) = 2.001091569589103 absolute error = 1.577271646624467e-11 relative error = 7.882056326567337e-10 % Correct digits = 11 h = 1e-05 x2[1] (analytic) = 1.000725769507762 x2[1] (numeric) = 1.000725769473705 absolute error = 3.405742354800623e-11 relative error = 3.40327236349259e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5001799999999992 x1[1] (analytic) = 2.001091558689234 x1[1] (numeric) = 2.001091558671551 absolute error = 1.768274415780979e-11 relative error = 8.836549272834093e-10 % Correct digits = 11 h = 1e-05 x2[1] (analytic) = 1.000725778565422 x2[1] (numeric) = 1.00072577852724 absolute error = 3.818212412909361e-11 relative error = 3.815443245983841e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5001899999999991 x1[1] (analytic) = 2.001091547773702 x1[1] (numeric) = 2.001091547754 absolute error = 1.970246188420788e-11 relative error = 9.845857330279412e-10 % Correct digits = 11 h = 1e-05 x2[1] (analytic) = 1.000725787623318 x2[1] (numeric) = 1.000725787580775 absolute error = 4.254263608061137e-11 relative error = 4.251178155571304e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5001999999999991 x1[1] (analytic) = 2.001091536858279 x1[1] (numeric) = 2.001091536836448 absolute error = 2.183098146701923e-11 relative error = 1.090953665282796e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.00072579668145 x2[1] (numeric) = 1.000725796634311 absolute error = 4.713895940255952e-11 relative error = 4.710477091614814e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.500209999999999 x1[1] (analytic) = 2.001091525942965 x1[1] (numeric) = 2.001091525918896 absolute error = 2.406874699545369e-11 relative error = 1.202780916485661e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000725805739817 x2[1] (numeric) = 1.000725805687846 absolute error = 5.197087205033313e-11 relative error = 5.193317865118117e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.500219999999999 x1[1] (analytic) = 2.00109151502776 x1[1] (numeric) = 2.001091515001344 absolute error = 2.641575846951127e-11 relative error = 1.320067486725854e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.00072581479842 x2[1] (numeric) = 1.000725814741381 absolute error = 5.703859606853712e-11 relative error = 5.699722663797439e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.500229999999999 x1[1] (analytic) = 2.001091504112664 x1[1] (numeric) = 2.001091504083793 absolute error = 2.887157179998212e-11 relative error = 1.44279118374372e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000725823857259 x2[1] (numeric) = 1.000725823794916 absolute error = 6.234213145717149e-11 relative error = 6.229691487012515e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5002399999999989 x1[1] (analytic) = 2.001091493197678 x1[1] (numeric) = 2.001091493166241 absolute error = 3.143707516528593e-11 relative error = 1.570996392326396e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000725832916333 x2[1] (numeric) = 1.000725832848452 absolute error = 6.788125617163132e-11 relative error = 6.783202145767594e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5002499999999989 x1[1] (analytic) = 2.001091482282801 x1[1] (numeric) = 2.001091482248689 absolute error = 3.411138038700301e-11 relative error = 1.70463872786513e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000725841975643 x2[1] (numeric) = 1.000725841901987 absolute error = 7.365641430112646e-11 relative error = 7.36029901613345e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5002599999999988 x1[1] (analytic) = 2.001091471368032 x1[1] (numeric) = 2.001091471331137 absolute error = 3.68949315543432e-11 relative error = 1.843740382798206e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000725851035189 x2[1] (numeric) = 1.000725850955522 absolute error = 7.966693971184213e-11 relative error = 7.960915532403966e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5002699999999988 x1[1] (analytic) = 2.001091460453373 x1[1] (numeric) = 2.001091460413586 absolute error = 3.978728457809666e-11 relative error = 1.988279164865475e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000725860094971 x2[1] (numeric) = 1.000725860009057 absolute error = 8.591349853759311e-11 relative error = 8.585118259004494e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5002799999999987 x1[1] (analytic) = 2.001091449538823 x1[1] (numeric) = 2.001091449496034 absolute error = 4.278932763668308e-11 relative error = 2.138299458855038e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000725869154988 x2[1] (numeric) = 1.000725869062593 absolute error = 9.239564668916955e-11 relative error = 9.232862818584707e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5002899999999987 x1[1] (analytic) = 2.001091438624382 x1[1] (numeric) = 2.001091438578482 absolute error = 4.590017255168277e-11 relative error = 2.293756880157165e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000725878215242 x2[1] (numeric) = 1.000725878116128 absolute error = 9.91138282557813e-11 relative error = 9.904193587213635e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5002999999999986 x1[1] (analytic) = 2.001091427710051 x1[1] (numeric) = 2.00109142766093 absolute error = 4.912026341230558e-11 relative error = 2.454673621210619e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000725887275731 x2[1] (numeric) = 1.000725887169663 absolute error = 1.060675991482185e-10 relative error = 1.059906618754169e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5003099999999986 x1[1] (analytic) = 2.001091416795828 x1[1] (numeric) = 2.001091416743379 absolute error = 5.24496002185515e-11 relative error = 2.6210496821047e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000725896336456 x2[1] (numeric) = 1.000725896223198 absolute error = 1.132571814110861e-10 relative error = 1.131750280728298e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5003199999999985 x1[1] (analytic) = 2.001091405881715 x1[1] (numeric) = 2.001091405825827 absolute error = 5.588773888121068e-11 relative error = 2.792862870578648e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000725905397416 x2[1] (numeric) = 1.000725905276734 absolute error = 1.206825750443841e-10 relative error = 1.205950344579694e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5003299999999985 x1[1] (analytic) = 2.00109139496771 x1[1] (numeric) = 2.001091394908275 absolute error = 5.943512348949298e-11 relative error = 2.970135379071581e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000725914458612 x2[1] (numeric) = 1.000725914330269 absolute error = 1.283435580035075e-10 relative error = 1.282504591408934e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5003399999999985 x1[1] (analytic) = 2.001091384053815 x1[1] (numeric) = 2.001091383990723 absolute error = 6.30917540433984e-11 relative error = 3.152867207672794e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000725923520045 x2[1] (numeric) = 1.000725923383804 absolute error = 1.362405743776662e-10 relative error = 1.361417458822703e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5003499999999984 x1[1] (analytic) = 2.001091373140029 x1[1] (numeric) = 2.001091373073172 absolute error = 6.685763054292693e-11 relative error = 3.341058356471585e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000725932581713 x2[1] (numeric) = 1.000725932437339 absolute error = 1.443734021222554e-10 relative error = 1.442686727921551e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5003599999999984 x1[1] (analytic) = 2.001091362226353 x1[1] (numeric) = 2.00109136215562 absolute error = 7.073275298807857e-11 relative error = 3.534708825557244e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000725941643617 x2[1] (numeric) = 1.000725941490875 absolute error = 1.527420412372749e-10 relative error = 1.526312398641406e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5003699999999983 x1[1] (analytic) = 2.001091351312785 x1[1] (numeric) = 2.001091351238068 absolute error = 7.471667728964348e-11 relative error = 3.733796422668399e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000725950705756 x2[1] (numeric) = 1.00072595054441 absolute error = 1.613464917227247e-10 relative error = 1.612294470918197e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5003799999999983 x1[1] (analytic) = 2.001091340399326 x1[1] (numeric) = 2.001091340320516 absolute error = 7.880984753683151e-11 relative error = 3.938343340244763e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000725959768132 x2[1] (numeric) = 1.000725959597945 absolute error = 1.70186753578605e-10 relative error = 1.700632944687847e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5003899999999982 x1[1] (analytic) = 2.001091329485977 x1[1] (numeric) = 2.001091329402965 absolute error = 8.301226372964265e-11 relative error = 4.148349578375622e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000725968830743 x2[1] (numeric) = 1.00072596865148 absolute error = 1.792626047603108e-10 relative error = 1.791325601051032e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5003999999999982 x1[1] (analytic) = 2.001091318572736 x1[1] (numeric) = 2.001091318485413 absolute error = 8.732348177886706e-11 relative error = 4.363792944799235e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.00072597789359 x2[1] (numeric) = 1.000725977705016 absolute error = 1.885744893570518e-10 relative error = 1.884376877614177e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5004099999999981 x1[1] (analytic) = 2.001091307659606 x1[1] (numeric) = 2.001091307567861 absolute error = 9.174438986292444e-11 relative error = 4.584717824306823e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000725986956673 x2[1] (numeric) = 1.000725986758551 absolute error = 1.981221853242232e-10 relative error = 1.979784555477932e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5004199999999981 x1[1] (analytic) = 2.001091296746583 x1[1] (numeric) = 2.001091296650309 absolute error = 9.627409980339507e-11 relative error = 4.81107983228549e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000725996019992 x2[1] (numeric) = 1.000725995812086 absolute error = 2.07905692661825e-10 relative error = 2.077548634578207e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.500429999999998 x1[1] (analytic) = 2.00109128583367 x1[1] (numeric) = 2.001091285732758 absolute error = 1.00912611600279e-10 relative error = 5.042878968824153e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000726005083546 x2[1] (numeric) = 1.000726004865621 absolute error = 2.179250113698572e-10 relative error = 2.177669114850908e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.500439999999998 x1[1] (analytic) = 2.001091274920867 x1[1] (numeric) = 2.001091274815206 absolute error = 1.056608134319958e-10 relative error = 5.280159618714754e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000726014147337 x2[1] (numeric) = 1.000726013919157 absolute error = 2.281801414483198e-10 relative error = 2.28014599623194e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.500449999999998 x1[1] (analytic) = 2.001091264008172 x1[1] (numeric) = 2.001091263897654 absolute error = 1.10517817120126e-10 relative error = 5.522877397343666e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000726023211363 x2[1] (numeric) = 1.000726022972692 absolute error = 2.386710828972127e-10 relative error = 2.384979278657202e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5004599999999979 x1[1] (analytic) = 2.001091253095586 x1[1] (numeric) = 2.001091252980102 absolute error = 1.154840667538792e-10 relative error = 5.771054497151554e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000726032275625 x2[1] (numeric) = 1.000726032026227 absolute error = 2.49398057761141e-10 relative error = 2.492171180897695e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5004699999999979 x1[1] (analytic) = 2.00109124218311 x1[1] (numeric) = 2.001091242062551 absolute error = 1.205595623332556e-10 relative error = 6.024690918227694e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000726041340123 x2[1] (numeric) = 1.000726041079762 absolute error = 2.603608439954996e-10 relative error = 2.601719484054169e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5004799999999978 x1[1] (analytic) = 2.001091231270743 x1[1] (numeric) = 2.001091231144999 absolute error = 1.257438597690452e-10 relative error = 6.283764468309361e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000726050404857 x2[1] (numeric) = 1.000726050133298 absolute error = 2.715594416002887e-10 relative error = 2.713624188062514e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5004899999999978 x1[1] (analytic) = 2.001091220358485 x1[1] (numeric) = 2.001091220227447 absolute error = 1.31037403150458e-10 relative error = 6.548297339837578e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000726059469827 x2[1] (numeric) = 1.000726059186833 absolute error = 2.829936285309032e-10 relative error = 2.827883074023574e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5004999999999977 x1[1] (analytic) = 2.001091209446336 x1[1] (numeric) = 2.001091209309895 absolute error = 1.364401924774938e-10 relative error = 6.818289532901615e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000726068535032 x2[1] (numeric) = 1.000726068240368 absolute error = 2.946640709211579e-10 relative error = 2.944502798378362e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5005099999999977 x1[1] (analytic) = 2.001091198534296 x1[1] (numeric) = 2.001091198392344 absolute error = 1.419522277501528e-10 relative error = 7.093741047590738e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000726077600474 x2[1] (numeric) = 1.000726077293904 absolute error = 3.06570324681843e-10 relative error = 3.06347892339263e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5005199999999976 x1[1] (analytic) = 2.001091187622365 x1[1] (numeric) = 2.001091187474792 absolute error = 1.475730648792251e-10 relative error = 7.37462969164173e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000726086666151 x2[1] (numeric) = 1.000726086347439 absolute error = 3.187121677683535e-10 relative error = 3.184809230167277e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5005299999999976 x1[1] (analytic) = 2.001091176710543 x1[1] (numeric) = 2.00109117655724 absolute error = 1.533031479539204e-10 relative error = 7.660977657496095e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000726095732064 x2[1] (numeric) = 1.000726095400974 absolute error = 3.310900442698994e-10 relative error = 3.308498156308157e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5005399999999975 x1[1] (analytic) = 2.001091165798831 x1[1] (numeric) = 2.001091165639688 absolute error = 1.591424769742389e-10 relative error = 7.952784945243091e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000726104798213 x2[1] (numeric) = 1.000726104454509 absolute error = 3.437039541864806e-10 relative error = 3.434545701751082e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5005499999999975 x1[1] (analytic) = 2.001091154887227 x1[1] (numeric) = 2.001091154722137 absolute error = 1.650906078509706e-10 relative error = 8.250029362619136e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000726113864598 x2[1] (numeric) = 1.000726113508045 absolute error = 3.565534534288872e-10 relative error = 3.562947428762014e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5005599999999975 x1[1] (analytic) = 2.001091143975733 x1[1] (numeric) = 2.001091143804585 absolute error = 1.711479846733255e-10 relative error = 8.552733102066089e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000726122931219 x2[1] (numeric) = 1.00072612256158 absolute error = 3.696389860863292e-10 relative error = 3.693707774946682e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5005699999999974 x1[1] (analytic) = 2.001091133064348 x1[1] (numeric) = 2.001091132887033 absolute error = 1.773146074413035e-10 relative error = 8.860896163673204e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000726131998076 x2[1] (numeric) = 1.000726131615115 absolute error = 3.829605521588064e-10 relative error = 3.826826740240884e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5005799999999974 x1[1] (analytic) = 2.001091122153072 x1[1] (numeric) = 2.001091121969481 absolute error = 1.835904761549045e-10 relative error = 9.174518547529738e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000726141065168 x2[1] (numeric) = 1.00072614066865 absolute error = 3.965179296017141e-10 relative error = 3.962302105745556e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5005899999999973 x1[1] (analytic) = 2.001091111241905 x1[1] (numeric) = 2.00109111105193 absolute error = 1.899751467249189e-10 relative error = 9.493578061371613e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000726150132496 x2[1] (numeric) = 1.000726149722186 absolute error = 4.103108963704472e-10 relative error = 4.100131652561711e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5005999999999973 x1[1] (analytic) = 2.001091100330847 x1[1] (numeric) = 2.001091100134378 absolute error = 1.964690632405564e-10 relative error = 9.818096897641166e-09 % Correct digits = 10 h = 1e-05 x2[1] (analytic) = 1.000726159200061 x2[1] (numeric) = 1.000726158775721 absolute error = 4.243401185988205e-10 relative error = 4.240322037129722e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5006099999999972 x1[1] (analytic) = 2.001091089419898 x1[1] (numeric) = 2.001091089216826 absolute error = 2.030722257018169e-10 relative error = 1.014807505642765e-08 % Correct digits = 9 h = 1e-05 x2[1] (analytic) = 1.000726168267861 x2[1] (numeric) = 1.000726167829256 absolute error = 4.386053742422291e-10 relative error = 4.382871040550515e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5006199999999972 x1[1] (analytic) = 2.001091078509059 x1[1] (numeric) = 2.001091078299274 absolute error = 2.097841900194908e-10 relative error = 1.048349034546661e-08 % Correct digits = 9 h = 1e-05 x2[1] (analytic) = 1.000726177335898 x2[1] (numeric) = 1.000726176882791 absolute error = 4.531062192114632e-10 relative error = 4.52777422509031e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5006299999999971 x1[1] (analytic) = 2.001091067598328 x1[1] (numeric) = 2.001091067381723 absolute error = 2.166054002827877e-10 relative error = 1.082436495720075e-08 % Correct digits = 9 h = 1e-05 x2[1] (analytic) = 1.00072618640417 x2[1] (numeric) = 1.000726185936327 absolute error = 4.678430975957326e-10 relative error = 4.675036028354532e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5006399999999971 x1[1] (analytic) = 2.001091056687707 x1[1] (numeric) = 2.001091056464171 absolute error = 2.235358564917078e-10 relative error = 1.117069889171931e-08 % Correct digits = 9 h = 1e-05 x2[1] (analytic) = 1.000726195472678 x2[1] (numeric) = 1.000726194989862 absolute error = 4.828160093950373e-10 relative error = 4.824656450278955e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.500649999999997 x1[1] (analytic) = 2.001091045777194 x1[1] (numeric) = 2.001091045546619 absolute error = 2.305751145570412e-10 relative error = 1.152246995675747e-08 % Correct digits = 9 h = 1e-05 x2[1] (analytic) = 1.000726204541422 x2[1] (numeric) = 1.000726204043397 absolute error = 4.980247325647724e-10 relative error = 4.976633271964633e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.500659999999997 x1[1] (analytic) = 2.001091034866791 x1[1] (numeric) = 2.001091034629067 absolute error = 2.377236185679976e-10 relative error = 1.18797003447583e-08 % Correct digits = 9 h = 1e-05 x2[1] (analytic) = 1.000726213610402 x2[1] (numeric) = 1.000726213096932 absolute error = 5.134692671049379e-10 relative error = 5.130966493347396e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.500669999999997 x1[1] (analytic) = 2.001091023956497 x1[1] (numeric) = 2.001091023711516 absolute error = 2.449813685245772e-10 relative error = 1.224239005581102e-08 % Correct digits = 9 h = 1e-05 x2[1] (analytic) = 1.000726222679617 x2[1] (numeric) = 1.000726222150468 absolute error = 5.291498350601387e-10 relative error = 5.28765833319775e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5006799999999969 x1[1] (analytic) = 2.001091013046312 x1[1] (numeric) = 2.001091012793964 absolute error = 2.5234792033757e-10 relative error = 1.261051689765047e-08 % Correct digits = 9 h = 1e-05 x2[1] (analytic) = 1.000726231749069 x2[1] (numeric) = 1.000726231204003 absolute error = 5.450662143857699e-10 relative error = 5.446706572616801e-08 % Correct digits = 9 h = 1e-05 Finished! Maximum Time Reached before Solution Completed! diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1; Iterations = 68 Total Elapsed Time = 1 Minutes 1 Seconds Elapsed Time(since restart) = 1 Minutes 1 Seconds Expected Time Remaining = 4 Days 14 Hours 29 Minutes 25 Seconds Optimized Time Remaining = 4 Days 12 Hours 40 Minutes 44 Seconds Time to Timeout Unknown Percent Done = 0.01533 %