##############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=10000000; glob_max_minutes=3; 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 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 = 5.004093412037817e-152 estimated_step_error = 5.004093412037817e-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 = 6.811212724408108e-113 estimated_step_error = 6.811212724408108e-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 = 4.570923134360025e-105 estimated_step_error = 4.570923134360025e-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 = 3.067488750234022e-97 estimated_step_error = 3.067488750234022e-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 = 2.05854901161809e-89 estimated_step_error = 2.05854901161809e-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 = 1.381458319740244e-81 estimated_step_error = 1.381458319740244e-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 = 9.270668118428105e-74 estimated_step_error = 9.270668118428105e-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 = 6.221249002016115e-66 estimated_step_error = 6.221249002016115e-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 = 4.174750875079241e-58 estimated_step_error = 4.174750875079241e-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 = 2.801274754399603e-50 estimated_step_error = 2.801274754399603e-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 = 0.09579 Order of pole (three term test) = -1.134 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 0.1052 Order of pole (three term test) = -1.184 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 2.220446049250313e-16 relative error = 1.114229439445855e-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 = 0.1146 Order of pole (three term test) = -1.239 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 0.1239 Order of pole (three term test) = -1.299 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 0.1332 Order of pole (three term test) = -1.364 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 0.1425 Order of pole (three term test) = -1.433 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 4.440892098500626e-16 relative error = 2.234717757576804e-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 = 0.1517 Order of pole (three term test) = -1.507 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 4.440892098500626e-16 relative error = 2.236566361965296e-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 = 0.1608 Order of pole (three term test) = -1.585 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 0.1698 Order of pole (three term test) = -1.668 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 0.1788 Order of pole (three term test) = -1.755 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 0.1877 Order of pole (three term test) = -1.847 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y2[1] (analytic) = 0.7915401001539003 y2[1] (numeric) = 0.7915401001539004 absolute error = 1.110223024625157e-16 relative error = 1.402611218824282e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.978030914724148 y1[1] (numeric) = 1.978030914724148 absolute error = 4.440892098500626e-16 relative error = 2.245107528625225e-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 = 0.1966 Order of pole (three term test) = -1.943 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 0.2054 Order of pole (three term test) = -2.044 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 0.214 Order of pole (three term test) = -2.149 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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) = 1.97133797485203 y1[1] (numeric) = 1.971337974852029 absolute error = 6.661338147750939e-16 relative error = 3.379094925745011e-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 = 0.2226 Order of pole (three term test) = -2.259 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 6.661338147750939e-16 relative error = 3.383257718473525e-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 = 0.2311 Order of pole (three term test) = -2.373 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y2[1] (analytic) = 0.7429194481078448 y2[1] (numeric) = 0.7429194481078448 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.966389978134513 y1[1] (numeric) = 1.966389978134513 absolute error = 4.440892098500626e-16 relative error = 2.258398460062149e-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 = 0.2395 Order of pole (three term test) = -2.491 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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) = 1.96377089636589 y1[1] (numeric) = 1.96377089636589 absolute error = 4.440892098500626e-16 relative error = 2.26141048669111e-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 = 0.2479 Order of pole (three term test) = -2.613 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 6.661338147750939e-16 relative error = 3.396812766032221e-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 = 0.2561 Order of pole (three term test) = -2.739 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 6.661338147750939e-16 relative error = 3.401689764512554e-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 = 0.2642 Order of pole (three term test) = -2.87 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 0.2722 Order of pole (three term test) = -3.004 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 0.2801 Order of pole (three term test) = -3.143 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y2[1] (analytic) = 0.685433439383882 y2[1] (numeric) = 0.6854334393838822 absolute error = 2.220446049250313e-16 relative error = 3.2394772733093e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.949235418082441 y1[1] (numeric) = 1.94923541808244 absolute error = 4.440892098500626e-16 relative error = 2.278273859229047e-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 = 0.2879 Order of pole (three term test) = -3.285 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 0.2956 Order of pole (three term test) = -3.431 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 0.3031 Order of pole (three term test) = -3.581 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y2[1] (analytic) = 0.6571021925445485 y2[1] (numeric) = 0.6571021925445486 absolute error = 1.110223024625157e-16 relative error = 1.689574372482235e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.939372712847379 y1[1] (numeric) = 1.939372712847378 absolute error = 4.440892098500626e-16 relative error = 2.28986005066583e-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 = 0.3106 Order of pole (three term test) = -3.735 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y2[1] (analytic) = 0.6477257667249098 y2[1] (numeric) = 0.64772576672491 absolute error = 2.220446049250313e-16 relative error = 3.428065028935834e-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 = 0.3179 Order of pole (three term test) = -3.893 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y2[1] (analytic) = 0.6383845680350378 y2[1] (numeric) = 0.638384568035038 absolute error = 1.110223024625157e-16 relative error = 1.739113193231547e-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 = 0.325 Order of pole (three term test) = -4.054 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 4.440892098500626e-16 relative error = 2.302573509454726e-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 = 0.3321 Order of pole (three term test) = -4.219 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 0.339 Order of pole (three term test) = -4.387 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 2.220446049250313e-16 relative error = 1.155843596940462e-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 = 0.3458 Order of pole (three term test) = -4.559 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 0.3524 Order of pole (three term test) = -4.734 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 0.3589 Order of pole (three term test) = -4.912 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y2[1] (analytic) = 0.583129197570789 y2[1] (numeric) = 0.5831291975707892 absolute error = 2.220446049250313e-16 relative error = 3.807811473855692e-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 = 0.3653 Order of pole (three term test) = -5.093 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y2[1] (analytic) = 0.5740605349340001 y2[1] (numeric) = 0.5740605349340003 absolute error = 2.220446049250313e-16 relative error = 3.867964986489793e-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 = 0.3715 Order of pole (three term test) = -5.278 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y2[1] (analytic) = 0.5650344658887695 y2[1] (numeric) = 0.5650344658887697 absolute error = 2.220446049250313e-16 relative error = 3.929753286390536e-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 = 0.3776 Order of pole (three term test) = -5.466 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 0.3835 Order of pole (three term test) = -5.657 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y2[1] (analytic) = 0.5471137146209314 y2[1] (numeric) = 0.5471137146209316 absolute error = 2.220446049250313e-16 relative error = 4.058472653694585e-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 = 0.3892 Order of pole (three term test) = -5.85 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 = 0.3949 Order of pole (three term test) = -6.047 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y2[1] (analytic) = 0.5293741118288416 y2[1] (numeric) = 0.5293741118288419 absolute error = 2.220446049250313e-16 relative error = 4.194474190623497e-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 = 0.4003 Order of pole (three term test) = -6.246 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 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 Seconds Elapsed Time(since restart) = 0 Seconds Time to Timeout = 3 Minutes 0 Seconds Percent Done = 102.5 %