##############ECHO OF PROBLEM################# ##############temp/nonlinear1postode.ode################# diff ( y , x , 1 ) = y * y; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK // # problem from Boyce DePrima - // # _Elementary Differential Equations and Boundary Value Problems_ // # page 23 // # Singularity at x = 1 (which depends on init condition) // # 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=0.001; // # Not Given = 0 // # No Pole = 3 // # Pole = 4 glob_type_given_pole=4; // # Real Part array_given_rad_poles[1][1]=1.0; // # Imag Part array_given_rad_poles[1][2]=0.0; // # Order array_given_ord_poles[1][1]=0.0; // # Not Used array_given_ord_poles[1][2]=0.0; // 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_y (double x) { return(1.0/(1.0 - 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 = 0.5 estimated_steps = 500000 step_error = 2e-16 est_needed_step_err = 2e-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 = 1.00000050000025e-156 estimated_step_error = 1.00000050000025e-156 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 = 6.710893110893108e-149 estimated_step_error = 6.710893110893108e-149 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 = 4.503608634587763e-141 estimated_step_error = 4.503608634587763e-141 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 = 3.022326638343125e-133 estimated_step_error = 3.022326638343125e-133 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 = 2.028257186422657e-125 estimated_step_error = 2.028257186422657e-125 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 = 1.361151246103686e-117 estimated_step_error = 1.361151246103686e-117 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 = 9.134677542999217e-110 estimated_step_error = 9.134677542999217e-110 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 = 6.130374507430422e-102 estimated_step_error = 6.130374507430422e-102 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 = 4.114288022161223e-94 estimated_step_error = 4.114288022161223e-94 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 = 2.761405458467275e-86 estimated_step_error = 2.761405458467275e-86 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 = 1.853622482259314e-78 estimated_step_error = 1.853622482259314e-78 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (analytic) = 1 y[1] (numeric) = 1 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 651 Radius of convergence (six term test) for eq 1 = 0.4145 Order of pole (six term test) = -14.62 TOP MAIN SOLVE Loop x[1] = 0.01 y[1] (analytic) = 1.01010101010101 y[1] (numeric) = 1.010101010101011 absolute error = 4.440892098500626e-16 relative error = 4.39648317751562e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.99 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.99 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.99 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.02000000000000001 y[1] (analytic) = 1.020408163265306 y[1] (numeric) = 1.020408163265307 absolute error = 4.440892098500626e-16 relative error = 4.352074256530614e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.98 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.98 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.98 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.03000000000000002 y[1] (analytic) = 1.030927835051547 y[1] (numeric) = 1.030927835051547 absolute error = 6.661338147750939e-16 relative error = 6.46149800331841e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.97 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.97 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.97 Order of pole (three term test) = 651 Radius of convergence (six term test) for eq 1 = 0.09424 Order of pole (six term test) = -12.48 TOP MAIN SOLVE Loop x[1] = 0.04000000000000003 y[1] (analytic) = 1.041666666666667 y[1] (numeric) = 1.041666666666668 absolute error = 8.881784197001252e-16 relative error = 8.526512829121202e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.96 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.96 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.96 Order of pole (three term test) = 651 Radius of convergence (six term test) for eq 1 = 0.2288 Order of pole (six term test) = -11.99 TOP MAIN SOLVE Loop x[1] = 0.05000000000000004 y[1] (analytic) = 1.052631578947368 y[1] (numeric) = 1.05263157894737 absolute error = 1.332267629550188e-15 relative error = 1.265654248072678e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.95 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.95 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.95 Order of pole (three term test) = 651 Radius of convergence (six term test) for eq 1 = 0.1106 Order of pole (six term test) = -11.77 TOP MAIN SOLVE Loop x[1] = 0.06000000000000005 y[1] (analytic) = 1.063829787234043 y[1] (numeric) = 1.063829787234044 absolute error = 1.110223024625157e-15 relative error = 1.043609643147647e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.94 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.94 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.94 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.07000000000000005 y[1] (analytic) = 1.075268817204301 y[1] (numeric) = 1.075268817204302 absolute error = 6.661338147750939e-16 relative error = 6.195044477408372e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.93 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.93 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.93 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.08000000000000006 y[1] (analytic) = 1.086956521739131 y[1] (numeric) = 1.086956521739131 absolute error = 4.440892098500626e-16 relative error = 4.085620730620575e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.92 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.92 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.92 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09000000000000007 y[1] (analytic) = 1.098901098901099 y[1] (numeric) = 1.098901098901099 absolute error = 4.440892098500626e-16 relative error = 4.041211809635569e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.91 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.91 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.91 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1000000000000001 y[1] (analytic) = 1.111111111111111 y[1] (numeric) = 1.111111111111112 absolute error = 4.440892098500626e-16 relative error = 3.996802888650564e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.9 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1100000000000001 y[1] (analytic) = 1.123595505617978 y[1] (numeric) = 1.123595505617978 absolute error = 6.661338147750939e-16 relative error = 5.928590951498336e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.89 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.89 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.89 Order of pole (three term test) = 651 Radius of convergence (six term test) for eq 1 = 0.1757 Order of pole (six term test) = -12.25 TOP MAIN SOLVE Loop x[1] = 0.1200000000000001 y[1] (analytic) = 1.136363636363636 y[1] (numeric) = 1.136363636363637 absolute error = 4.440892098500626e-16 relative error = 3.90798504668055e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.88 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.88 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.88 Order of pole (three term test) = 651 Radius of convergence (six term test) for eq 1 = 0.3921 Order of pole (six term test) = -14.31 TOP MAIN SOLVE Loop x[1] = 0.1300000000000001 y[1] (analytic) = 1.149425287356322 y[1] (numeric) = 1.149425287356323 absolute error = 8.881784197001252e-16 relative error = 7.727152251391088e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.87 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.87 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.87 Order of pole (three term test) = 651 Radius of convergence (six term test) for eq 1 = 0.05597 Order of pole (six term test) = -12.13 TOP MAIN SOLVE Loop x[1] = 0.1400000000000001 y[1] (analytic) = 1.162790697674419 y[1] (numeric) = 1.16279069767442 absolute error = 8.881784197001252e-16 relative error = 7.638334409421077e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.86 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.86 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.86 Order of pole (three term test) = 651 Radius of convergence (six term test) for eq 1 = 0.3278 Order of pole (six term test) = -11.93 TOP MAIN SOLVE Loop x[1] = 0.1500000000000001 y[1] (analytic) = 1.176470588235294 y[1] (numeric) = 1.176470588235295 absolute error = 1.110223024625157e-15 relative error = 9.436895709313831e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.85 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.85 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.85 Order of pole (three term test) = 651 Radius of convergence (six term test) for eq 1 = 0.1288 Order of pole (six term test) = -12.56 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (analytic) = 1.190476190476191 y[1] (numeric) = 1.190476190476191 absolute error = 4.440892098500626e-16 relative error = 3.730349362740525e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.84 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.84 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.84 Order of pole (three term test) = 651 Radius of convergence (six term test) for eq 1 = 0.07934 Order of pole (six term test) = -12.4 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (analytic) = 1.204819277108434 y[1] (numeric) = 1.204819277108434 absolute error = 4.440892098500626e-16 relative error = 3.685940441755519e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.83 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.83 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.83 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (analytic) = 1.219512195121951 y[1] (numeric) = 1.219512195121952 absolute error = 4.440892098500626e-16 relative error = 3.641531520770513e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.82 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.82 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.82 Order of pole (three term test) = 651 Radius of convergence (six term test) for eq 1 = 0.3002 Order of pole (six term test) = -12.39 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (analytic) = 1.234567901234568 y[1] (numeric) = 1.234567901234568 absolute error = 4.440892098500626e-16 relative error = 3.597122599785507e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.81 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.81 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.81 Order of pole (three term test) = 651 Radius of convergence (six term test) for eq 1 = 0.06981 Order of pole (six term test) = -11.67 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y[1] (analytic) = 1.25 y[1] (numeric) = 1.25 absolute error = 2.220446049250313e-16 relative error = 1.77635683940025e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.8 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2100000000000002 y[1] (analytic) = 1.265822784810127 y[1] (numeric) = 1.265822784810127 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.79 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.79 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.79 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2200000000000002 y[1] (analytic) = 1.282051282051282 y[1] (numeric) = 1.282051282051282 absolute error = 2.220446049250313e-16 relative error = 1.731947918415244e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.78 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.78 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.78 Order of pole (three term test) = 651 Radius of convergence (six term test) for eq 1 = 0.06502 Order of pole (six term test) = -12.44 TOP MAIN SOLVE Loop x[1] = 0.2300000000000002 y[1] (analytic) = 1.298701298701299 y[1] (numeric) = 1.298701298701299 absolute error = 2.220446049250313e-16 relative error = 1.709743457922741e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.77 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.77 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.77 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2400000000000002 y[1] (analytic) = 1.315789473684211 y[1] (numeric) = 1.31578947368421 absolute error = 4.440892098500626e-16 relative error = 3.375077994860475e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.76 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.76 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.76 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2500000000000002 y[1] (analytic) = 1.333333333333334 y[1] (numeric) = 1.333333333333333 absolute error = 6.661338147750939e-16 relative error = 4.996003610813203e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.75 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.75 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.75 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2600000000000002 y[1] (analytic) = 1.351351351351352 y[1] (numeric) = 1.351351351351351 absolute error = 4.440892098500626e-16 relative error = 3.286260152890462e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.74 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.74 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.74 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2700000000000002 y[1] (analytic) = 1.369863013698631 y[1] (numeric) = 1.36986301369863 absolute error = 6.661338147750939e-16 relative error = 4.862776847858184e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.73 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.73 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.73 Order of pole (three term test) = 651 Radius of convergence (six term test) for eq 1 = 0.1384 Order of pole (six term test) = -13.34 TOP MAIN SOLVE Loop x[1] = 0.2800000000000002 y[1] (analytic) = 1.388888888888889 y[1] (numeric) = 1.388888888888888 absolute error = 1.110223024625157e-15 relative error = 7.993605777301125e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.72 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.72 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.72 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2900000000000002 y[1] (analytic) = 1.408450704225352 y[1] (numeric) = 1.408450704225351 absolute error = 1.332267629550188e-15 relative error = 9.459100169806331e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.71 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.71 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.71 Order of pole (three term test) = 651 Radius of convergence (six term test) for eq 1 = 0.2583 Order of pole (six term test) = -13.19 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (analytic) = 1.428571428571429 y[1] (numeric) = 1.428571428571427 absolute error = 1.77635683940025e-15 relative error = 1.243449787580175e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (analytic) = 1.449275362318841 y[1] (numeric) = 1.44927536231884 absolute error = 1.332267629550188e-15 relative error = 9.192646643896294e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.69 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.69 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.69 Order of pole (three term test) = 651 Radius of convergence (six term test) for eq 1 = 0.04269 Order of pole (six term test) = -11.48 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (analytic) = 1.470588235294118 y[1] (numeric) = 1.470588235294117 absolute error = 1.332267629550188e-15 relative error = 9.059419880941274e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.68 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.68 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.68 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (analytic) = 1.492537313432836 y[1] (numeric) = 1.492537313432835 absolute error = 1.554312234475219e-15 relative error = 1.041389197098396e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.67 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.67 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.67 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y[1] (analytic) = 1.515151515151516 y[1] (numeric) = 1.515151515151514 absolute error = 1.332267629550188e-15 relative error = 8.792966355031236e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.66 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.66 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.66 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3500000000000003 y[1] (analytic) = 1.538461538461539 y[1] (numeric) = 1.538461538461538 absolute error = 1.110223024625157e-15 relative error = 7.216449660063515e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.65 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.65 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.65 Order of pole (three term test) = 651 Radius of convergence (six term test) for eq 1 = 0.2583 Order of pole (six term test) = -14.16 TOP MAIN SOLVE Loop x[1] = 0.3600000000000003 y[1] (analytic) = 1.562500000000001 y[1] (numeric) = 1.562499999999999 absolute error = 1.554312234475219e-15 relative error = 9.947598300641399e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.64 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.64 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.64 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3700000000000003 y[1] (analytic) = 1.587301587301588 y[1] (numeric) = 1.587301587301587 absolute error = 1.110223024625157e-15 relative error = 6.994405055138484e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.63 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.63 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3800000000000003 y[1] (analytic) = 1.612903225806452 y[1] (numeric) = 1.612903225806451 absolute error = 1.332267629550188e-15 relative error = 8.260059303211161e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.62 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.62 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.62 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3900000000000003 y[1] (analytic) = 1.639344262295083 y[1] (numeric) = 1.639344262295082 absolute error = 8.881784197001252e-16 relative error = 5.417888360170761e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.61 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.61 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.61 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4000000000000003 y[1] (analytic) = 1.666666666666667 y[1] (numeric) = 1.666666666666666 absolute error = 1.110223024625157e-15 relative error = 6.661338147750937e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.6 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.6 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (analytic) = 1.694915254237289 y[1] (numeric) = 1.694915254237288 absolute error = 1.110223024625157e-15 relative error = 6.550315845288421e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.59 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.59 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.59 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (analytic) = 1.724137931034484 y[1] (numeric) = 1.724137931034483 absolute error = 1.110223024625157e-15 relative error = 6.439293542825904e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.58 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.58 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.58 Order of pole (three term test) = 651 Radius of convergence (six term test) for eq 1 = 0.08488 Order of pole (six term test) = -12 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y[1] (analytic) = 1.754385964912282 y[1] (numeric) = 1.754385964912281 absolute error = 8.881784197001252e-16 relative error = 5.062616992290711e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.57 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.57 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.57 Order of pole (three term test) = 651 Radius of convergence (six term test) for eq 1 = 0.07685 Order of pole (six term test) = -11.25 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y[1] (analytic) = 1.785714285714287 y[1] (numeric) = 1.785714285714286 absolute error = 1.110223024625157e-15 relative error = 6.217248937900873e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.56 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.56 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.56 Order of pole (three term test) = 651 Radius of convergence (six term test) for eq 1 = 0.3233 Order of pole (six term test) = -14.78 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y[1] (analytic) = 1.818181818181819 y[1] (numeric) = 1.818181818181818 absolute error = 8.881784197001252e-16 relative error = 4.884981308350686e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.55 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.55 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.55 Order of pole (three term test) = 651 Radius of convergence (six term test) for eq 1 = 0.08225 Order of pole (six term test) = -12.03 TOP MAIN SOLVE Loop x[1] = 0.4600000000000004 y[1] (analytic) = 1.851851851851853 y[1] (numeric) = 1.851851851851852 absolute error = 1.110223024625157e-15 relative error = 5.995204332975842e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.54 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.54 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.54 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4700000000000004 y[1] (analytic) = 1.88679245283019 y[1] (numeric) = 1.886792452830188 absolute error = 1.554312234475219e-15 relative error = 8.237854842718655e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.53 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.53 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.53 Order of pole (three term test) = 651 Radius of convergence (six term test) for eq 1 = 0.09935 Order of pole (six term test) = -11.85 TOP MAIN SOLVE Loop x[1] = 0.4800000000000004 y[1] (analytic) = 1.923076923076924 y[1] (numeric) = 1.923076923076923 absolute error = 1.110223024625157e-15 relative error = 5.77315972805081e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.52 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.52 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.52 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4900000000000004 y[1] (analytic) = 1.960784313725492 y[1] (numeric) = 1.96078431372549 absolute error = 1.554312234475219e-15 relative error = 7.926992395823611e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.51 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.51 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.51 Order of pole (three term test) = 651 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = y * y; Iterations = 500 Total Elapsed Time = 0 Seconds Elapsed Time(since restart) = 0 Seconds Time to Timeout = 3 Minutes 0 Seconds Percent Done = 100.2 %