##############ECHO OF PROBLEM################# ##############temp/nonlinear1postode.ode################# diff ( y , x , 1 ) = y * y ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=20 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb x_start=0.0 x_end=0.5 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=1000000 $glob_max_h=0.5 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=1 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=1.0 # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=0.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=0.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=0.0 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb #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_y (x) return(1.0/(1.0 - 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 0.5 estimated_steps 500000.0 step_error 2.0e-16 est_needed_step_err 2.0e-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 1.0000005000002499e-96 estimated_step_error 1.0000005000002499e-96 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 6.553606553606554e-92 estimated_step_error 6.553606553606554e-92 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 4.294975885951771e-87 estimated_step_error 4.294975885951771e-87 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 2.814761026150664e-82 estimated_step_error 2.814761026150664e-82 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 1.8446891648842738e-77 estimated_step_error 1.8446891648842738e-77 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 1.208945162737233e-72 estimated_step_error 1.208945162737233e-72 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 7.923069789659704e-68 estimated_step_error 7.923069789659704e-68 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 5.192629186802782e-63 estimated_step_error 5.192629186802782e-63 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 3.4032592863980424e-58 estimated_step_error 3.4032592863980424e-58 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 2.2306455651177226e-53 estimated_step_error 2.2306455651177226e-53 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 1.4622503094892607e-48 estimated_step_error 1.4622503094892607e-48 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 9.587915155520526e-44 estimated_step_error 9.587915155520526e-44 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 6.289983621733564e-39 estimated_step_error 6.289983621733564e-39 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 4.130680660128981e-34 estimated_step_error 4.130680660128981e-34 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 2.718262662302969e-29 estimated_step_error 2.718262662302969e-29 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 1.796277142160798e-24 estimated_step_error 1.796277142160798e-24 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 1.1971476929849968e-19 estimated_step_error 1.1971476929849968e-19 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 8.120602159323812e-15 estimated_step_error 8.120602159323812e-15 best_h 0.065536 START of Soultion TOP MAIN SOLVE Loop x[1] 0.0 y[1] (analytic) 1.0 y[1] (numeric) 1.0 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.9999999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.9999999999999928 Order of pole (three term test) 0.9999999999998763 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.01 y[1] (analytic) 1.0101010101010102 y[1] (numeric) 1.0101010101010102 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.99 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.9899999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.9899999999999891 Order of pole (three term test) 0.9999999999998379 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.02 y[1] (analytic) 1.0204081632653061 y[1] (numeric) 1.0204081632653061 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.98 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.98 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.9800000000000013 Order of pole (three term test) 1.0000000000000597 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.03 y[1] (analytic) 1.0309278350515465 y[1] (numeric) 1.0309278350515465 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.97 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.9699999999999996 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.969999999999999 Order of pole (three term test) 1.000000000000016 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.04 y[1] (analytic) 1.0416666666666667 y[1] (numeric) 1.0416666666666667 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.96 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.9599999999999996 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.9600000000000088 Order of pole (three term test) 1.000000000000155 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.05 y[1] (analytic) 1.0526315789473684 y[1] (numeric) 1.0526315789473686 absolute error 2.220446049250313e-16 relative error 2.1094237467877974e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.95 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.9499999999999996 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.950000000000002 Order of pole (three term test) 1.0000000000000575 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.060000000000000005 y[1] (analytic) 1.0638297872340425 y[1] (numeric) 1.0638297872340428 absolute error 2.220446049250313e-16 relative error 2.0872192862952943e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.94 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.9399999999999995 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.940000000000005 Order of pole (three term test) 1.0000000000000886 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.07 y[1] (analytic) 1.0752688172043012 y[1] (numeric) 1.0752688172043012 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.9299999999999999 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.9299999999999997 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.930000000000005 Order of pole (three term test) 1.0000000000000113 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.08 y[1] (analytic) 1.0869565217391304 y[1] (numeric) 1.0869565217391306 absolute error 2.220446049250313e-16 relative error 2.042810365310288e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.92 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.9199999999999995 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.9199999999999994 Order of pole (three term test) 0.9999999999999871 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.09 y[1] (analytic) 1.0989010989010988 y[1] (numeric) 1.098901098901099 absolute error 2.220446049250313e-16 relative error 2.0206059048177852e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.91 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.91 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.9100000000000006 Order of pole (three term test) 0.9999999999999895 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.09999999999999999 y[1] (analytic) 1.1111111111111112 y[1] (numeric) 1.1111111111111112 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.9 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.9000000000000001 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.900000000000004 Order of pole (three term test) 1.0000000000000544 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.10999999999999999 y[1] (analytic) 1.1235955056179776 y[1] (numeric) 1.1235955056179776 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.89 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.89 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.8900000000000022 Order of pole (three term test) 1.0000000000000266 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.11999999999999998 y[1] (analytic) 1.1363636363636365 y[1] (numeric) 1.1363636363636365 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.88 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.8799999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.8799999999999981 Order of pole (three term test) 0.9999999999999579 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.12999999999999998 y[1] (analytic) 1.1494252873563218 y[1] (numeric) 1.149425287356322 absolute error 2.220446049250313e-16 relative error 1.9317880628477724e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.87 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.87 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.8700000000000017 Order of pole (three term test) 0.9999999999999837 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.13999999999999999 y[1] (analytic) 1.1627906976744187 y[1] (numeric) 1.1627906976744187 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.86 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.8600000000000002 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.8599999999999967 Order of pole (three term test) 0.9999999999999564 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.15 y[1] (analytic) 1.1764705882352942 y[1] (numeric) 1.1764705882352942 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.85 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.85 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.8500000000000052 Order of pole (three term test) 1.0000000000000722 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.16 y[1] (analytic) 1.1904761904761905 y[1] (numeric) 1.1904761904761905 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.84 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.8400000000000003 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.8399999999999944 Order of pole (three term test) 0.9999999999999075 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.17 y[1] (analytic) 1.2048192771084338 y[1] (numeric) 1.2048192771084336 absolute error 2.220446049250313e-16 relative error 1.8429702208777595e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.83 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.8300000000000001 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.8300000000000068 Order of pole (three term test) 1.0000000000000946 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.18000000000000002 y[1] (analytic) 1.2195121951219512 y[1] (numeric) 1.2195121951219512 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.82 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.82 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.8199999999999983 Order of pole (three term test) 1.0000000000000093 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.19000000000000003 y[1] (analytic) 1.234567901234568 y[1] (numeric) 1.2345679012345678 absolute error 2.220446049250313e-16 relative error 1.7985612998927533e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.8099999999999999 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.8099999999999995 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.810000000000009 Order of pole (three term test) 1.0000000000001115 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.20000000000000004 y[1] (analytic) 1.25 y[1] (numeric) 1.25 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.7999999999999999 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.8 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.8000000000000043 Order of pole (three term test) 1.0000000000001157 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.21000000000000005 y[1] (analytic) 1.2658227848101267 y[1] (numeric) 1.2658227848101267 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.7899999999999999 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.7899999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.7900000000000083 Order of pole (three term test) 1.0000000000001301 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.22000000000000006 y[1] (analytic) 1.2820512820512822 y[1] (numeric) 1.2820512820512822 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.7799999999999999 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.7799999999999996 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.7800000000000035 Order of pole (three term test) 1.0000000000000715 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.23000000000000007 y[1] (analytic) 1.298701298701299 y[1] (numeric) 1.298701298701299 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.7699999999999999 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.7699999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.7700000000000062 Order of pole (three term test) 1.0000000000000906 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.24000000000000007 y[1] (analytic) 1.3157894736842106 y[1] (numeric) 1.3157894736842108 absolute error 2.220446049250313e-16 relative error 1.687538997430238e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.7599999999999999 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.7600000000000001 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.7600000000000067 Order of pole (three term test) 1.0000000000001372 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.25000000000000006 y[1] (analytic) 1.3333333333333333 y[1] (numeric) 1.3333333333333337 absolute error 4.440892098500626e-16 relative error 3.3306690738754696e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.75 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.7499999999999996 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.750000000000008 Order of pole (three term test) 1.000000000000119 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.26000000000000006 y[1] (analytic) 1.3513513513513513 y[1] (numeric) 1.3513513513513518 absolute error 4.440892098500626e-16 relative error 3.2862601528904634e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.74 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.7399999999999995 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.7400000000000013 Order of pole (three term test) 1.0000000000000195 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2700000000000001 y[1] (analytic) 1.36986301369863 y[1] (numeric) 1.3698630136986305 absolute error 4.440892098500626e-16 relative error 3.241851231905457e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.73 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.73 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.7300000000000026 Order of pole (three term test) 1.000000000000009 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2800000000000001 y[1] (analytic) 1.3888888888888888 y[1] (numeric) 1.3888888888888893 absolute error 4.440892098500626e-16 relative error 3.197442310920451e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.72 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.7199999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.7199999999999971 Order of pole (three term test) 0.9999999999999281 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2900000000000001 y[1] (analytic) 1.4084507042253522 y[1] (numeric) 1.4084507042253525 absolute error 2.220446049250313e-16 relative error 1.5765166949677223e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.71 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.71 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.7099999999999983 Order of pole (three term test) 0.9999999999999557 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3000000000000001 y[1] (analytic) 1.4285714285714286 y[1] (numeric) 1.4285714285714288 absolute error 2.220446049250313e-16 relative error 1.554312234475219e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.7 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.7000000000000001 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.6999999999999981 Order of pole (three term test) 0.9999999999999529 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3100000000000001 y[1] (analytic) 1.4492753623188408 y[1] (numeric) 1.4492753623188408 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.69 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.6899999999999996 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.6900000000000075 Order of pole (three term test) 1.000000000000109 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3200000000000001 y[1] (analytic) 1.4705882352941178 y[1] (numeric) 1.470588235294118 absolute error 2.220446049250313e-16 relative error 1.509903313490213e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.6799999999999999 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.6799999999999997 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.6799999999999945 Order of pole (three term test) 0.9999999999998701 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3300000000000001 y[1] (analytic) 1.492537313432836 y[1] (numeric) 1.4925373134328361 absolute error 2.220446049250313e-16 relative error 1.4876988529977098e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.6699999999999999 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.6699999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.6700000000000023 Order of pole (three term test) 1.0000000000000175 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.34000000000000014 y[1] (analytic) 1.5151515151515154 y[1] (numeric) 1.5151515151515156 absolute error 2.220446049250313e-16 relative error 1.4654943925052063e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.6599999999999999 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.6599999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.6599999999999998 Order of pole (three term test) 0.9999999999999931 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.35000000000000014 y[1] (analytic) 1.5384615384615388 y[1] (numeric) 1.538461538461539 absolute error 2.220446049250313e-16 relative error 1.4432899320127032e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.6499999999999999 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.6499999999999996 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.6500000000000018 Order of pole (three term test) 1.000000000000017 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.36000000000000015 y[1] (analytic) 1.5625000000000002 y[1] (numeric) 1.5625000000000004 absolute error 2.220446049250313e-16 relative error 1.4210854715202002e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.6399999999999999 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.6399999999999997 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.6400000000000003 Order of pole (three term test) 0.9999999999999917 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.37000000000000016 y[1] (analytic) 1.5873015873015877 y[1] (numeric) 1.5873015873015877 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.6299999999999999 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.63 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.6300000000000047 Order of pole (three term test) 1.0000000000001095 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.38000000000000017 y[1] (analytic) 1.612903225806452 y[1] (numeric) 1.612903225806452 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.6199999999999999 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.6199999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.6200000000000009 Order of pole (three term test) 1.0000000000000093 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3900000000000002 y[1] (analytic) 1.6393442622950822 y[1] (numeric) 1.6393442622950822 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.6099999999999999 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.6099999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.6100000000000015 Order of pole (three term test) 1.0000000000000628 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4000000000000002 y[1] (analytic) 1.666666666666667 y[1] (numeric) 1.666666666666667 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.5999999999999999 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.5999999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.6000000000000039 Order of pole (three term test) 1.0000000000000606 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4100000000000002 y[1] (analytic) 1.6949152542372885 y[1] (numeric) 1.6949152542372885 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.5899999999999999 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.5899999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.5899999999999949 Order of pole (three term test) 0.9999999999998729 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4200000000000002 y[1] (analytic) 1.7241379310344833 y[1] (numeric) 1.724137931034483 absolute error 2.220446049250313e-16 relative error 1.2878587085651811e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.5799999999999998 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.5799999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.5800000000000017 Order of pole (three term test) 1.0000000000000613 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4300000000000002 y[1] (analytic) 1.7543859649122813 y[1] (numeric) 1.754385964912281 absolute error 2.220446049250313e-16 relative error 1.265654248072678e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.5699999999999998 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.5699999999999996 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.5700000000000056 Order of pole (three term test) 1.0000000000001183 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4400000000000002 y[1] (analytic) 1.7857142857142863 y[1] (numeric) 1.785714285714286 absolute error 2.220446049250313e-16 relative error 1.243449787580175e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.5599999999999998 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.56 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.5599999999999976 Order of pole (three term test) 0.9999999999999449 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.45000000000000023 y[1] (analytic) 1.8181818181818188 y[1] (numeric) 1.8181818181818186 absolute error 2.220446049250313e-16 relative error 1.2212453270876717e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.5499999999999998 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.5499999999999996 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.550000000000002 Order of pole (three term test) 1.000000000000034 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.46000000000000024 y[1] (analytic) 1.8518518518518525 y[1] (numeric) 1.8518518518518523 absolute error 2.220446049250313e-16 relative error 1.1990408665951686e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.5399999999999998 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.5399999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.5400000000000015 Order of pole (three term test) 1.0000000000000167 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.47000000000000025 y[1] (analytic) 1.8867924528301894 y[1] (numeric) 1.8867924528301891 absolute error 2.220446049250313e-16 relative error 1.1768364061026655e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.5299999999999998 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.5299999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.5300000000000042 Order of pole (three term test) 1.0000000000001101 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.48000000000000026 y[1] (analytic) 1.9230769230769238 y[1] (numeric) 1.9230769230769236 absolute error 2.220446049250313e-16 relative error 1.1546319456101623e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.5199999999999998 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.5199999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.5199999999999996 Order of pole (three term test) 0.9999999999999863 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.49000000000000027 y[1] (analytic) 1.960784313725491 y[1] (numeric) 1.9607843137254908 absolute error 2.220446049250313e-16 relative error 1.1324274851176592e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.5099999999999998 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.5099999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.5099999999999992 Order of pole (three term test) 1.0000000000000098 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = y * y ; Iterations 50 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 10 Minutes 0.0 Seconds Percent Done 102.00000000000004%