##############ECHO OF PROBLEM################# ##############temp/mtest3postode.ode################# diff ( y2 , x , 1 ) = m1 * y1 + 1.0 ; diff ( y1 , x , 1 ) = y2 - 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=0.5; array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); glob_max_iter=20; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=1000000000; glob_max_minutes=10.0; glob_subiter_method=3; /* 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 Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 400000.0000000001 step_error = 2.5e-16 est_needed_step_err = 2.5e-16 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.467208605532302e-183 estimated_step_error = 2.467208605532302e-183 best_h = 2e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.655715664606566e-175 estimated_step_error = 1.655715664606566e-175 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.111131969458436e-167 estimated_step_error = 1.111131969458436e-167 best_h = 8e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.456680367024186e-160 estimated_step_error = 7.456680367024186e-160 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.004093412037816e-152 estimated_step_error = 5.004093412037816e-152 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.358190142481624e-144 estimated_step_error = 3.358190142481624e-144 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.25364312158092e-136 estimated_step_error = 2.25364312158092e-136 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.512394117654307e-128 estimated_step_error = 1.512394117654307e-128 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.014950270158055e-120 estimated_step_error = 1.014950270158055e-120 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.811212724408107e-113 estimated_step_error = 6.811212724408107e-113 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.570923134360028e-105 estimated_step_error = 4.570923134360028e-105 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.067488750234037e-97 estimated_step_error = 3.067488750234037e-97 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.058549011618171e-89 estimated_step_error = 2.058549011618171e-89 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.381458319740679e-81 estimated_step_error = 1.381458319740679e-81 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.27066811845143e-74 estimated_step_error = 9.27066811845143e-74 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.221249002141341e-66 estimated_step_error = 6.221249002141341e-66 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.174750875751544e-58 estimated_step_error = 4.174750875751544e-58 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.801274758009002e-50 estimated_step_error = 2.801274758009002e-50 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y2[1] (analytic) = 0.9001665833531718 y2[1] (numeric) = 0.9001665833531718 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.995004165278026 y1[1] (numeric) = 1.995004165278026 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09933 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09933 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.11 y2[1] (analytic) = 0.8902216991628252 y2[1] (numeric) = 0.8902216991628251 absolute error = 1.110223024625157e-16 relative error = 1.247130940157068e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.993956097956697 y1[1] (numeric) = 1.993956097956697 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1091 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1091 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.12 y2[1] (analytic) = 0.8802877927110806 y2[1] (numeric) = 0.8802877927110806 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.992808635853866 y1[1] (numeric) = 1.992808635853866 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1189 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1189 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.13 y2[1] (analytic) = 0.8703658573803051 y2[1] (numeric) = 0.8703658573803051 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.991561893714788 y1[1] (numeric) = 1.991561893714788 absolute error = 2.220446049250313e-16 relative error = 1.114926960722569e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1285 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1285 Order of pole (three term test) = 22.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.14 y2[1] (analytic) = 0.8604568853557635 y2[1] (numeric) = 0.8604568853557635 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.990215996212637 y1[1] (numeric) = 1.990215996212637 absolute error = 2.220446049250313e-16 relative error = 1.115680937886039e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1382 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1382 Order of pole (three term test) = 22.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.15 y2[1] (analytic) = 0.8505618675264007 y2[1] (numeric) = 0.8505618675264007 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.988771077936042 y1[1] (numeric) = 1.988771077936042 absolute error = 4.440892098500626e-16 relative error = 2.232983045544593e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1478 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1478 Order of pole (three term test) = 22.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.16 y2[1] (analytic) = 0.840681793385754 y2[1] (numeric) = 0.840681793385754 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.987227283375627 y1[1] (numeric) = 1.987227283375627 absolute error = 2.220446049250313e-16 relative error = 1.117358878788402e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1573 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1573 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.17 y2[1] (analytic) = 0.830817650933004 y2[1] (numeric) = 0.830817650933004 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.985584766909561 y1[1] (numeric) = 1.98558476690956 absolute error = 2.220446049250313e-16 relative error = 1.118283180982648e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1667 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1667 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.18 y2[1] (analytic) = 0.8209704265741757 y2[1] (numeric) = 0.8209704265741758 absolute error = 1.110223024625157e-16 relative error = 1.352330106771327e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.983843692788121 y1[1] (numeric) = 1.983843692788121 absolute error = 2.220446049250313e-16 relative error = 1.119264616119866e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1761 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1761 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y2[1] (analytic) = 0.8111411050234993 y2[1] (numeric) = 0.8111411050234995 absolute error = 1.110223024625157e-16 relative error = 1.368717499026255e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.98200423511727 y1[1] (numeric) = 1.98200423511727 absolute error = 4.440892098500626e-16 relative error = 2.240606765523823e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1855 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1855 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y2[1] (analytic) = 0.8013306692049387 y2[1] (numeric) = 0.8013306692049388 absolute error = 1.110223024625157e-16 relative error = 1.38547427084838e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.980066577841242 y1[1] (numeric) = 1.980066577841241 absolute error = 4.440892098500626e-16 relative error = 2.242799382706761e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1947 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1947 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y2[1] (analytic) = 0.7915401001539004 y2[1] (numeric) = 0.7915401001539004 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.978030914724148 y1[1] (numeric) = 1.978030914724148 absolute error = 6.661338147750939e-16 relative error = 3.367661292937838e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2039 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2039 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y2[1] (analytic) = 0.7817703769191306 y2[1] (numeric) = 0.7817703769191306 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.975897449330605 y1[1] (numeric) = 1.975897449330605 absolute error = 4.440892098500626e-16 relative error = 2.247531672256124e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.213 Order of pole (three term test) = 22.95 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.213 Order of pole (three term test) = 22.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y2[1] (analytic) = 0.7720224764648115 y2[1] (numeric) = 0.7720224764648116 absolute error = 1.110223024625157e-16 relative error = 1.438070857352506e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.973666395005375 y1[1] (numeric) = 1.973666395005374 absolute error = 4.440892098500626e-16 relative error = 2.250072306920204e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.222 Order of pole (three term test) = 22.95 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.222 Order of pole (three term test) = 22.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y2[1] (analytic) = 0.7622973735728653 y2[1] (numeric) = 0.7622973735728654 absolute error = 1.110223024625157e-16 relative error = 1.456417223926109e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.971337974852029 y1[1] (numeric) = 1.971337974852029 absolute error = 4.440892098500626e-16 relative error = 2.252729950496674e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2309 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2309 Order of pole (three term test) = 22.06 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y2[1] (analytic) = 0.7525960407454769 y2[1] (numeric) = 0.752596040745477 absolute error = 1.110223024625157e-16 relative error = 1.475191157696545e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.968912421710645 y1[1] (numeric) = 1.968912421710644 absolute error = 4.440892098500626e-16 relative error = 2.255505145649017e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2397 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2397 Order of pole (three term test) = 22.06 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y2[1] (analytic) = 0.7429194481078447 y2[1] (numeric) = 0.7429194481078448 absolute error = 1.110223024625157e-16 relative error = 1.494405655219828e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.966389978134513 y1[1] (numeric) = 1.966389978134513 absolute error = 6.661338147750939e-16 relative error = 3.387597690093222e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2484 Order of pole (three term test) = 22.93 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2484 Order of pole (three term test) = 22.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y2[1] (analytic) = 0.7332685633111687 y2[1] (numeric) = 0.7332685633111689 absolute error = 1.110223024625157e-16 relative error = 1.514074215334967e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.963770896365891 y1[1] (numeric) = 1.96377089636589 absolute error = 6.661338147750939e-16 relative error = 3.392115730036665e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2571 Order of pole (three term test) = 22.93 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2571 Order of pole (three term test) = 22.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y2[1] (analytic) = 0.7236443514358861 y2[1] (numeric) = 0.7236443514358862 absolute error = 1.110223024625157e-16 relative error = 1.534210862590448e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.961055438310771 y1[1] (numeric) = 1.96105543831077 absolute error = 4.440892098500626e-16 relative error = 2.264541844021481e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2656 Order of pole (three term test) = 22.92 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2656 Order of pole (three term test) = 22.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y2[1] (analytic) = 0.7140477748951644 y2[1] (numeric) = 0.7140477748951645 absolute error = 1.110223024625157e-16 relative error = 1.554830171956153e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.958243875512697 y1[1] (numeric) = 1.958243875512697 absolute error = 4.440892098500626e-16 relative error = 2.267793176341703e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.274 Order of pole (three term test) = 22.92 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.274 Order of pole (three term test) = 22.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y2[1] (analytic) = 0.7044797933386603 y2[1] (numeric) = 0.7044797933386604 absolute error = 1.110223024625157e-16 relative error = 1.575947294901964e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.955336489125606 y1[1] (numeric) = 1.955336489125605 absolute error = 6.661338147750939e-16 relative error = 3.40674773104131e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2823 Order of pole (three term test) = 22.91 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2823 Order of pole (three term test) = 22.09 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y2[1] (analytic) = 0.6949413635565563 y2[1] (numeric) = 0.6949413635565564 absolute error = 1.110223024625157e-16 relative error = 1.597577986930121e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.952333569885713 y1[1] (numeric) = 1.952333569885713 absolute error = 6.661338147750939e-16 relative error = 3.411987710758302e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2905 Order of pole (three term test) = 22.91 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2905 Order of pole (three term test) = 22.09 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y2[1] (analytic) = 0.6854334393838821 y2[1] (numeric) = 0.6854334393838822 absolute error = 1.110223024625157e-16 relative error = 1.619738636654649e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.949235418082441 y1[1] (numeric) = 1.94923541808244 absolute error = 6.661338147750939e-16 relative error = 3.417410788843569e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2986 Order of pole (three term test) = 22.9 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2986 Order of pole (three term test) = 22.1 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y2[1] (analytic) = 0.6759569716051315 y2[1] (numeric) = 0.6759569716051317 absolute error = 2.220446049250313e-16 relative error = 3.284892593056077e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.946042343528387 y1[1] (numeric) = 1.946042343528386 absolute error = 4.440892098500626e-16 relative error = 2.282012060667089e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3066 Order of pole (three term test) = 22.89 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3066 Order of pole (three term test) = 22.11 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y2[1] (analytic) = 0.6665129078591854 y2[1] (numeric) = 0.6665129078591856 absolute error = 2.220446049250313e-16 relative error = 3.331437430645272e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.942754665528346 y1[1] (numeric) = 1.942754665528346 absolute error = 4.440892098500626e-16 relative error = 2.285873855972902e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3144 Order of pole (three term test) = 22.89 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3144 Order of pole (three term test) = 22.11 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y2[1] (analytic) = 0.6571021925445484 y2[1] (numeric) = 0.6571021925445486 absolute error = 2.220446049250313e-16 relative error = 3.379148744964471e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.939372712847379 y1[1] (numeric) = 1.939372712847378 absolute error = 6.661338147750939e-16 relative error = 3.434790075998744e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3221 Order of pole (three term test) = 22.88 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3221 Order of pole (three term test) = 22.12 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y2[1] (analytic) = 0.6477257667249099 y2[1] (numeric) = 0.64772576672491 absolute error = 1.110223024625157e-16 relative error = 1.714032514467917e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.935896823677935 y1[1] (numeric) = 1.935896823677934 absolute error = 4.440892098500626e-16 relative error = 2.293971478326799e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3297 Order of pole (three term test) = 22.88 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3297 Order of pole (three term test) = 22.12 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y2[1] (analytic) = 0.6383845680350377 y2[1] (numeric) = 0.638384568035038 absolute error = 2.220446049250313e-16 relative error = 3.478226386463095e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.932327345606034 y1[1] (numeric) = 1.932327345606034 absolute error = 4.440892098500626e-16 relative error = 2.298209000974332e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3371 Order of pole (three term test) = 22.87 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3371 Order of pole (three term test) = 22.13 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y2[1] (analytic) = 0.6290795305870172 y2[1] (numeric) = 0.6290795305870173 absolute error = 1.110223024625157e-16 relative error = 1.764837306960484e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.92866463557651 y1[1] (numeric) = 1.92866463557651 absolute error = 2.220446049250313e-16 relative error = 1.151286754727363e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3445 Order of pole (three term test) = 22.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3445 Order of pole (three term test) = 22.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y2[1] (analytic) = 0.6198115848768384 y2[1] (numeric) = 0.6198115848768385 absolute error = 1.110223024625157e-16 relative error = 1.791226643247991e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.924909059857313 y1[1] (numeric) = 1.924909059857313 absolute error = 2.220446049250313e-16 relative error = 1.153532961923358e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3516 Order of pole (three term test) = 22.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3516 Order of pole (three term test) = 22.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y2[1] (analytic) = 0.6105816576913493 y2[1] (numeric) = 0.6105816576913494 absolute error = 1.110223024625157e-16 relative error = 1.818303924855825e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.921060994002885 y1[1] (numeric) = 1.921060994002885 absolute error = 4.440892098500626e-16 relative error = 2.311687193880923e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3587 Order of pole (three term test) = 22.85 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3587 Order of pole (three term test) = 22.15 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y2[1] (analytic) = 0.6013906720155768 y2[1] (numeric) = 0.6013906720155771 absolute error = 2.220446049250313e-16 relative error = 3.692185716496781e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.917120822816605 y1[1] (numeric) = 1.917120822816605 absolute error = 2.220446049250313e-16 relative error = 1.158219149687221e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3656 Order of pole (three term test) = 22.84 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3656 Order of pole (three term test) = 22.16 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y2[1] (analytic) = 0.5922395469404296 y2[1] (numeric) = 0.5922395469404298 absolute error = 2.220446049250313e-16 relative error = 3.749236370183933e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.913088940312308 y1[1] (numeric) = 1.913088940312308 absolute error = 2.220446049250313e-16 relative error = 1.16066012534045e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3723 Order of pole (three term test) = 22.83 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3723 Order of pole (three term test) = 22.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y2[1] (analytic) = 0.5831291975707891 y2[1] (numeric) = 0.5831291975707892 absolute error = 1.110223024625157e-16 relative error = 1.903905736927846e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.908965749674885 y1[1] (numeric) = 1.908965749674885 absolute error = 2.220446049250313e-16 relative error = 1.163167044578184e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3789 Order of pole (three term test) = 22.83 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3789 Order of pole (three term test) = 22.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y2[1] (analytic) = 0.5740605349340002 y2[1] (numeric) = 0.5740605349340003 absolute error = 1.110223024625157e-16 relative error = 1.933982493244896e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.904751663219963 y1[1] (numeric) = 1.904751663219963 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3854 Order of pole (three term test) = 22.82 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3854 Order of pole (three term test) = 22.18 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y2[1] (analytic) = 0.5650344658887696 y2[1] (numeric) = 0.5650344658887697 absolute error = 1.110223024625157e-16 relative error = 1.964876643195268e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.900447102352677 y1[1] (numeric) = 1.900447102352677 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3917 Order of pole (three term test) = 22.81 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3917 Order of pole (three term test) = 22.19 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y2[1] (analytic) = 0.55605189303448 y2[1] (numeric) = 0.5560518930344801 absolute error = 1.110223024625157e-16 relative error = 1.996617651216796e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.896052497525525 y1[1] (numeric) = 1.896052497525525 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3978 Order of pole (three term test) = 22.8 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3978 Order of pole (three term test) = 22.2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y2[1] (analytic) = 0.5471137146209315 y2[1] (numeric) = 0.5471137146209316 absolute error = 1.110223024625157e-16 relative error = 2.029236326847292e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.891568288195329 y1[1] (numeric) = 1.891568288195329 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4038 Order of pole (three term test) = 22.79 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4038 Order of pole (three term test) = 22.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y2[1] (analytic) = 0.5382208244585168 y2[1] (numeric) = 0.538220824458517 absolute error = 2.220446049250313e-16 relative error = 4.125529798079103e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.886994922779284 y1[1] (numeric) = 1.886994922779284 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4096 Order of pole (three term test) = 22.79 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4096 Order of pole (three term test) = 22.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y2[1] (analytic) = 0.5293741118288418 y2[1] (numeric) = 0.5293741118288419 absolute error = 1.110223024625157e-16 relative error = 2.097237095311748e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.882332858610121 y1[1] (numeric) = 1.882332858610122 absolute error = 2.220446049250313e-16 relative error = 1.179624548917373e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4152 Order of pole (three term test) = 22.78 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4152 Order of pole (three term test) = 22.22 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y2 , x , 1 ) = m1 * y1 + 1.0 ; diff ( y1 , x , 1 ) = y2 - 1.0 ; Iterations = 40 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 102.5 %