##############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; ELIMINATED in preodein.rb 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 def exact_soln_y1 (x) return(1.0 + cos(x)) end def exact_soln_y2 (x) return(1.0 - sin(x)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 10 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-10 range 0.4 estimated_steps 400000.00000000006 step_error 2.4999999999999997e-16 est_needed_step_err 2.4999999999999997e-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 2.4672086055323017e-183 estimated_step_error 2.4672086055323017e-183 best_h 2.0e-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 1.6557156646065657e-175 estimated_step_error 1.6557156646065657e-175 best_h 4.0e-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 1.1111319694584355e-167 estimated_step_error 1.1111319694584355e-167 best_h 8.0e-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 1.5123941176543068e-128 estimated_step_error 1.5123941176543068e-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 1.0149502701580555e-120 estimated_step_error 1.0149502701580555e-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 2.0585490116181713e-89 estimated_step_error 2.0585490116181713e-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 1.3814583197406789e-81 estimated_step_error 1.3814583197406789e-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 2.8012747580090023e-50 estimated_step_error 2.8012747580090023e-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 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.9950041652780257 y1[1] (numeric) 1.9950041652780257 absolute error 0.0 relative error 0.0% 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 0.09933466539753057 Order of pole (three term test) 22.990033288920625 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 0.09933466539753057 Order of pole (three term test) 22.009966711079382 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 1.1102230246251565e-16 relative error 1.2471309401570678e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9939560979566968 y1[1] (numeric) 1.9939560979566968 absolute error 0.0 relative error 0.0% 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 0.10911481154043479 Order of pole (three term test) 22.9879487246653 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 0.10911481154043476 Order of pole (three term test) 22.0120512753347 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 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.9928086358538661 y1[1] (numeric) 1.9928086358538661 absolute error 0.0 relative error 0.0% 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 0.11885131321356733 Order of pole (three term test) 22.985668987426013 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 0.11885131321356733 Order of pole (three term test) 22.014331012573983 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 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.991561893714788 y1[1] (numeric) 1.9915618937147879 absolute error 2.220446049250313e-16 relative error 1.1149269607225692e-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 0.1285402759460775 Order of pole (three term test) 22.983194989067254 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 0.12854027594607748 Order of pole (three term test) 22.01680501093274 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 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.9902159962126371 y1[1] (numeric) 1.990215996212637 absolute error 2.220446049250313e-16 relative error 1.1156809378860393e-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 0.13817782428205697 Order of pole (three term test) 22.980527719155383 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 0.13817782428205694 Order of pole (three term test) 22.019472280844614 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.15000000000000002 y2[1] (analytic) 0.8505618675264007 y2[1] (numeric) 0.8505618675264007 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.9887710779360424 y1[1] (numeric) 1.988771077936042 absolute error 4.440892098500626e-16 relative error 2.2329830455445925e-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 0.1477601033306699 Order of pole (three term test) 22.977668244562803 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 0.14776010333066988 Order of pole (three term test) 22.022331755437193 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.16000000000000003 y2[1] (analytic) 0.840681793385754 y2[1] (numeric) 0.840681793385754 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.9872272833756268 y1[1] (numeric) 1.9872272833756266 absolute error 2.220446049250313e-16 relative error 1.1173588787884023e-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 0.15728328030805885 Order of pole (three term test) 22.97461770904122 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 0.15728328030805883 Order of pole (three term test) 22.025382290958774 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.17000000000000004 y2[1] (analytic) 0.830817650933004 y2[1] (numeric) 0.830817650933004 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.9855847669095605 y1[1] (numeric) 1.9855847669095603 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 0.16674354607040726 Order of pole (three term test) 22.971377332764174 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 0.16674354607040726 Order of pole (three term test) 22.02862266723583 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.18000000000000005 y2[1] (analytic) 0.8209704265741757 y2[1] (numeric) 0.8209704265741758 absolute error 1.1102230246251565e-16 relative error 1.3523301067713265e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9838436927881213 y1[1] (numeric) 1.9838436927881211 absolute error 2.220446049250313e-16 relative error 1.1192646161198656e-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 0.176137116637545 Order of pole (three term test) 22.967948411838968 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 0.17613711663754503 Order of pole (three term test) 22.032051588161035 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.19000000000000006 y2[1] (analytic) 0.8111411050234993 y2[1] (numeric) 0.8111411050234995 absolute error 1.1102230246251565e-16 relative error 1.3687174990262546e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9820042351172704 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 0.18546023470649148 Order of pole (three term test) 22.964332317788262 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 0.18546023470649145 Order of pole (three term test) 22.035667682211745 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.20000000000000007 y2[1] (analytic) 0.8013306692049387 y2[1] (numeric) 0.8013306692049388 absolute error 1.1102230246251565e-16 relative error 1.3854742708483797e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9800665778412416 y1[1] (numeric) 1.9800665778412412 absolute error 4.440892098500626e-16 relative error 2.2427993827067613e-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 0.19470917115432534 Order of pole (three term test) 22.960530497001443 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 0.19470917115432523 Order of pole (three term test) 22.039469502998557 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.21000000000000008 y2[1] (analytic) 0.7915401001539004 y2[1] (numeric) 0.7915401001539004 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.9780309147241484 y1[1] (numeric) 1.9780309147241477 absolute error 6.661338147750939e-16 relative error 3.3676612929378375e-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 0.2038802265297853 Order of pole (three term test) 22.956544470156157 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 0.20388022652978524 Order of pole (three term test) 22.043455529843847 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.22000000000000008 y2[1] (analytic) 0.7817703769191306 y2[1] (numeric) 0.7817703769191306 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.9758974493306054 y1[1] (numeric) 1.975897449330605 absolute error 4.440892098500626e-16 relative error 2.2475316722561242e-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 0.2129697325329999 Order of pole (three term test) 22.95237583160998 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 0.2129697325329999 Order of pole (three term test) 22.04762416839002 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 1.1102230246251565e-16 relative error 1.4380708573525064e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9736663950053748 y1[1] (numeric) 1.9736663950053743 absolute error 4.440892098500626e-16 relative error 2.2500723069202038e-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 0.22197405348275995 Order of pole (three term test) 22.948026248762762 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 0.22197405348275995 Order of pole (three term test) 22.051973751237238 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 1.1102230246251565e-16 relative error 1.456417223926109e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9713379748520294 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 0.23088958777074156 Order of pole (three term test) 22.943497461389644 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 0.2308895877707415 Order of pole (three term test) 22.056502538610356 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 1.1102230246251565e-16 relative error 1.4751911576965454e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9689124217106446 y1[1] (numeric) 1.9689124217106442 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 0.23971276930210153 Order of pole (three term test) 22.93879128094518 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 0.2397127693021016 Order of pole (three term test) 22.06120871905481 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 1.1102230246251565e-16 relative error 1.4944056552198278e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9663899781345133 y1[1] (numeric) 1.9663899781345127 absolute error 6.661338147750939e-16 relative error 3.3875976900932224e-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 0.24844006892186846 Order of pole (three term test) 22.933909589838823 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 0.24844006892186846 Order of pole (three term test) 22.066090410161177 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.27000000000000013 y2[1] (analytic) 0.7332685633111687 y2[1] (numeric) 0.7332685633111689 absolute error 1.1102230246251565e-16 relative error 1.5140742153349673e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9637708963658906 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 0.25706799582655676 Order of pole (three term test) 22.92885434068191 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 0.2570679958265568 Order of pole (three term test) 22.07114565931809 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.28000000000000014 y2[1] (analytic) 0.7236443514358861 y2[1] (numeric) 0.7236443514358862 absolute error 1.1102230246251565e-16 relative error 1.5342108625904485e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9610554383107708 y1[1] (numeric) 1.9610554383107703 absolute error 4.440892098500626e-16 relative error 2.2645418440214808e-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 0.265593098960442 Order of pole (three term test) 22.92362755550671 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 0.265593098960442 Order of pole (three term test) 22.07637244449329 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.29000000000000015 y2[1] (analytic) 0.7140477748951644 y2[1] (numeric) 0.7140477748951645 absolute error 1.1102230246251565e-16 relative error 1.5548301719561526e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.958243875512697 y1[1] (numeric) 1.9582438755126965 absolute error 4.440892098500626e-16 relative error 2.2677931763417034e-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 0.274011968395937 Order of pole (three term test) 22.918231324957592 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 0.27401196839593694 Order of pole (three term test) 22.081768675042404 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.30000000000000016 y2[1] (analytic) 0.7044797933386603 y2[1] (numeric) 0.7044797933386604 absolute error 1.1102230246251565e-16 relative error 1.5759472949019644e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.955336489125606 y1[1] (numeric) 1.9553364891256053 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 0.28232123669751763 Order of pole (three term test) 22.912667807454838 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 0.2823212366975177 Order of pole (three term test) 22.087332192545162 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.31000000000000016 y2[1] (analytic) 0.6949413635565563 y2[1] (numeric) 0.6949413635565564 absolute error 1.1102230246251565e-16 relative error 1.5975779869301208e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9523335698857134 y1[1] (numeric) 1.9523335698857127 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 0.29051758026865293 Order of pole (three term test) 22.906939228331268 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 0.2905175802686528 Order of pole (three term test) 22.09306077166874 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 1.1102230246251565e-16 relative error 1.6197386366546495e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.949235418082441 y1[1] (numeric) 1.9492354180824403 absolute error 6.661338147750939e-16 relative error 3.4174107888435693e-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 0.2985977206811963 Order of pole (three term test) 22.901047878942144 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 0.29859772068119633 Order of pole (three term test) 22.098952121057856 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) 1.9460423435283865 absolute error 4.440892098500626e-16 relative error 2.2820120606670893e-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 0.30655842598671695 Order of pole (three term test) 22.894996115748683 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 0.306558425986717 Order of pole (three term test) 22.105003884251317 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 3.3314374306452715e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.942754665528346 y1[1] (numeric) 1.9427546655283456 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 0.31439651200923435 Order of pole (three term test) 22.888786359375455 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 0.31439651200923435 Order of pole (three term test) 22.111213640624534 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) 1.9393727128473783 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 0.32210884361884584 Order of pole (three term test) 22.88242109364224 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 0.3221088436188459 Order of pole (three term test) 22.117578906357757 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 1.1102230246251565e-16 relative error 1.7140325144679168e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9358968236779348 y1[1] (numeric) 1.9358968236779344 absolute error 4.440892098500626e-16 relative error 2.2939714783267988e-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 0.32969233598573666 Order of pole (three term test) 22.875902864570445 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 0.32969233598573666 Order of pole (three term test) 22.124097135429547 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) 1.9323273456060344 y1[1] (numeric) 1.932327345606034 absolute error 4.440892098500626e-16 relative error 2.2982090009743315e-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 0.3371439558140726 Order of pole (three term test) 22.86923427936479 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 0.33714395581407264 Order of pole (three term test) 22.130765720635207 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 1.1102230246251565e-16 relative error 1.7648373069604838e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.92866463557651 y1[1] (numeric) 1.9286646355765098 absolute error 2.220446049250313e-16 relative error 1.1512867547273633e-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 0.3444607225552758 Order of pole (three term test) 22.86241800537045 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 0.3444607225552758 Order of pole (three term test) 22.137581994629546 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.39000000000000024 y2[1] (analytic) 0.6198115848768384 y2[1] (numeric) 0.6198115848768385 absolute error 1.1102230246251565e-16 relative error 1.791226643247991e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9249090598573129 y1[1] (numeric) 1.9249090598573126 absolute error 2.220446049250313e-16 relative error 1.1535329619233583e-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 0.35163970960020535 Order of pole (three term test) 22.85545676900614 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 0.35163970960020535 Order of pole (three term test) 22.14454323099386 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.40000000000000024 y2[1] (analytic) 0.6105816576913493 y2[1] (numeric) 0.6105816576913494 absolute error 1.1102230246251565e-16 relative error 1.8183039248558254e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.921060994002885 y1[1] (numeric) 1.9210609940028847 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 0.3586780454497616 Order of pole (three term test) 22.84835335467358 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 0.35867804544976156 Order of pole (three term test) 22.151646645326416 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.41000000000000025 y2[1] (analytic) 0.6013906720155768 y2[1] (numeric) 0.601390672015577 absolute error 2.220446049250313e-16 relative error 3.6921857164967806e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.917120822816605 y1[1] (numeric) 1.9171208228166048 absolute error 2.220446049250313e-16 relative error 1.1582191496872207e-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 0.36557291486344784 Order of pole (three term test) 22.841110603643806 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 0.3655729148634479 Order of pole (three term test) 22.158889396356194 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.42000000000000026 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) 1.9130889403123081 y1[1] (numeric) 1.913088940312308 absolute error 2.220446049250313e-16 relative error 1.1606601253404505e-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 0.3723215599854299 Order of pole (three term test) 22.833731412920653 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 0.3723215599854298 Order of pole (three term test) 22.166268587079347 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.43000000000000027 y2[1] (analytic) 0.5831291975707891 y2[1] (numeric) 0.5831291975707892 absolute error 1.1102230246251565e-16 relative error 1.9039057369278458e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.908965749674885 y1[1] (numeric) 1.9089657496748849 absolute error 2.220446049250313e-16 relative error 1.1631670445781838e-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 0.37892128144763854 Order of pole (three term test) 22.826218734082026 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 0.3789212814476385 Order of pole (three term test) 22.173781265917974 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 1.1102230246251565e-16 relative error 1.933982493244896e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9047516632199633 y1[1] (numeric) 1.9047516632199633 absolute error 0.0 relative error 0.0% 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 0.38536943944948465 Order of pole (three term test) 22.818575572099288 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 0.3853694394494847 Order of pole (three term test) 22.18142442790071 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 1.1102230246251565e-16 relative error 1.9648766431952677e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9004471023526768 y1[1] (numeric) 1.9004471023526768 absolute error 0.0 relative error 0.0% 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 0.39166345481374176 Order of pole (three term test) 22.81080498413533 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 0.3916634548137418 Order of pole (three term test) 22.18919501586467 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 1.1102230246251565e-16 relative error 1.996617651216796e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.896052497525525 y1[1] (numeric) 1.896052497525525 absolute error 0.0 relative error 0.0% 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 0.39780081001818296 Order of pole (three term test) 22.802910078321734 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 0.3978008100181829 Order of pole (three term test) 22.19708992167827 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 1.1102230246251565e-16 relative error 2.029236326847292e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8915682881953289 y1[1] (numeric) 1.8915682881953289 absolute error 0.0 relative error 0.0% 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 0.403779050202557 Order of pole (three term test) 22.794894012515545 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 0.403779050202557 Order of pole (three term test) 22.205105987484448 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) 1.8869949227792842 y1[1] (numeric) 1.8869949227792842 absolute error 0.0 relative error 0.0% 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 0.4095957841504991 Order of pole (three term test) 22.786759993036224 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 0.4095957841504991 Order of pole (three term test) 22.21324000696377 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 1.1102230246251565e-16 relative error 2.097237095311748e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8823328586101213 y1[1] (numeric) 1.8823328586101216 absolute error 2.220446049250313e-16 relative error 1.1796245489173727e-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 0.4152486852459853 Order of pole (three term test) 22.77851127338311 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 0.41524868524598535 Order of pole (three term test) 22.221488726616894 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 1 Seconds Elapsed Time(since restart) 1 Seconds Time to Timeout 9 Minutes 59.0 Seconds Percent Done 102.50000000000009%