##############ECHO OF PROBLEM################# ##############temp/sing2postode.ode################# diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=50; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=-2.0; x_end=-1.5; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=100; // # Not Given = 0 // # No Pole = 3 // # Pole = 4 glob_type_given_pole=4; // # Real Part array_given_rad_poles[1][1]=0.0; // # Imag Part array_given_rad_poles[1][2]=1.0; // # Order array_given_ord_poles[1][1]=1.0; // # 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(arctan(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 = 1.122918524106954e-294 estimated_step_error = 1.122918524106954e-294 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 = 7.901837192668374e-281 estimated_step_error = 7.901837192668374e-281 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 = 5.560424383554312e-267 estimated_step_error = 5.560424383554312e-267 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 = 3.912801913190595e-253 estimated_step_error = 3.912801913190595e-253 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 = 2.753391121553642e-239 estimated_step_error = 2.753391121553642e-239 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 = 1.937528940289823e-225 estimated_step_error = 1.937528940289823e-225 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 = 1.363417859492428e-211 estimated_step_error = 1.363417859492428e-211 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 = 9.594243547696055e-198 estimated_step_error = 9.594243547696055e-198 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 = 6.751409621872924e-184 estimated_step_error = 6.751409621872924e-184 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 = 4.750967898646173e-170 estimated_step_error = 4.750967898646173e-170 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 = 3.343317078970731e-156 estimated_step_error = 3.343317078970731e-156 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 = 2.35281994225615e-142 estimated_step_error = 2.35281994225615e-142 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 = 1.655888466081137e-128 estimated_step_error = 1.655888466081137e-128 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 = 1.165563151162475e-114 estimated_step_error = 1.165563151162475e-114 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 = 8.20662274863913e-101 estimated_step_error = 8.20662274863913e-101 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 = 5.781466606566095e-87 estimated_step_error = 5.781466606566095e-87 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 = 4.077458109265972e-73 estimated_step_error = 4.077458109265972e-73 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 = 2.881707429125343e-59 estimated_step_error = 2.881707429125343e-59 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = -2 y[1] (analytic) = -1.10714871779409 y[1] (numeric) = -1.10714871779409 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.236 Order of pole (six term test) = -2.677e-12 TOP MAIN SOLVE Loop x[1] = -1.99 y[1] (analytic) = -1.105140688364494 y[1] (numeric) = -1.105140688364494 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.227 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.227 Order of pole (six term test) = -9.048e-12 TOP MAIN SOLVE Loop x[1] = -1.98 y[1] (analytic) = -1.103116481582997 y[1] (numeric) = -1.103116481582997 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.218 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.218 Order of pole (six term test) = -5.372e-12 TOP MAIN SOLVE Loop x[1] = -1.97 y[1] (analytic) = -1.101075917953986 y[1] (numeric) = -1.101075917953986 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.209 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.209 Order of pole (six term test) = -7.802e-12 TOP MAIN SOLVE Loop x[1] = -1.96 y[1] (analytic) = -1.099018815614146 y[1] (numeric) = -1.099018815614147 absolute error = 2.220446049250313e-16 relative error = 2.020389476234306e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.2 Order of pole (six term test) = -6.594e-12 TOP MAIN SOLVE Loop x[1] = -1.95 y[1] (analytic) = -1.096944990300136 y[1] (numeric) = -1.096944990300136 absolute error = 2.220446049250313e-16 relative error = 2.024209116122381e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.191 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.191 Order of pole (six term test) = -7.243e-12 TOP MAIN SOLVE Loop x[1] = -1.94 y[1] (analytic) = -1.094854255315938 y[1] (numeric) = -1.094854255315938 absolute error = 2.220446049250313e-16 relative error = 2.028074548250778e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.183 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.183 Order of pole (six term test) = -5.264e-12 TOP MAIN SOLVE Loop x[1] = -1.93 y[1] (analytic) = -1.092746421499885 y[1] (numeric) = -1.092746421499886 absolute error = 4.440892098500626e-16 relative error = 4.06397313331407e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.174 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.174 Order of pole (six term test) = -4.313e-12 TOP MAIN SOLVE Loop x[1] = -1.92 y[1] (analytic) = -1.09062129719137 y[1] (numeric) = -1.09062129719137 absolute error = 2.220446049250313e-16 relative error = 2.035945983237749e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.165 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.007821 Order of pole (three term test) = -2.832 Radius of convergence (six term test) for eq 1 = 2.165 Order of pole (six term test) = -7.303e-12 TOP MAIN SOLVE Loop x[1] = -1.91 y[1] (analytic) = -1.088478688197237 y[1] (numeric) = -1.088478688197237 absolute error = 4.440892098500626e-16 relative error = 4.079907256480817e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.156 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01177 Order of pole (three term test) = -8.531 Radius of convergence (six term test) for eq 1 = 2.156 Order of pole (six term test) = -7.134e-12 TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (analytic) = -1.086318397757873 y[1] (numeric) = -1.086318397757874 absolute error = 4.440892098500626e-16 relative error = 4.088020701542463e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.147 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01164 Order of pole (three term test) = -17.87 Radius of convergence (six term test) for eq 1 = 2.147 Order of pole (six term test) = -5.757e-12 TOP MAIN SOLVE Loop x[1] = -1.89 y[1] (analytic) = -1.084140226512997 y[1] (numeric) = -1.084140226512997 absolute error = 4.440892098500626e-16 relative error = 4.09623403863927e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.138 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.007435 Order of pole (three term test) = -30.58 Radius of convergence (six term test) for eq 1 = 2.138 Order of pole (six term test) = -2.561e-12 TOP MAIN SOLVE Loop x[1] = -1.88 y[1] (analytic) = -1.081943972467149 y[1] (numeric) = -1.081943972467149 absolute error = 6.661338147750939e-16 relative error = 6.156823566899809e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.129 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.129 Order of pole (six term test) = 3.96e-11 TOP MAIN SOLVE Loop x[1] = -1.87 y[1] (analytic) = -1.079729430954907 y[1] (numeric) = -1.079729430954907 absolute error = 4.440892098500626e-16 relative error = 4.112967537221919e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.121 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 0.908 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.121 Order of pole (six term test) = -3.46e-12 TOP MAIN SOLVE Loop x[1] = -1.86 y[1] (analytic) = -1.077496394605818 y[1] (numeric) = -1.077496394605818 absolute error = 4.440892098500626e-16 relative error = 4.121491376428453e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.112 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 0.5939 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.112 Order of pole (six term test) = -1.73e-12 TOP MAIN SOLVE Loop x[1] = -1.85 y[1] (analytic) = -1.075244653309068 y[1] (numeric) = -1.075244653309068 absolute error = 4.440892098500626e-16 relative error = 4.130122465462879e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.103 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.103 Order of pole (six term test) = -9.53e-13 TOP MAIN SOLVE Loop x[1] = -1.84 y[1] (analytic) = -1.072973994177895 y[1] (numeric) = -1.072973994177896 absolute error = 4.440892098500626e-16 relative error = 4.13886275212402e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.094 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.094 Order of pole (six term test) = -1.33e-12 TOP MAIN SOLVE Loop x[1] = -1.83 y[1] (analytic) = -1.070684201513757 y[1] (numeric) = -1.070684201513757 absolute error = 4.440892098500626e-16 relative error = 4.147714230042804e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.085 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.085 Order of pole (six term test) = 5.651e-12 TOP MAIN SOLVE Loop x[1] = -1.82 y[1] (analytic) = -1.068375056770266 y[1] (numeric) = -1.068375056770266 absolute error = 2.220446049250313e-16 relative error = 2.078339470001103e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.077 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.077 Order of pole (six term test) = 3.45e-12 TOP MAIN SOLVE Loop x[1] = -1.81 y[1] (analytic) = -1.066046338516909 y[1] (numeric) = -1.066046338516909 absolute error = 4.440892098500626e-16 relative error = 4.165758971302154e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 0.9297 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.068 Order of pole (six term test) = 2.275e-12 TOP MAIN SOLVE Loop x[1] = -1.8 y[1] (analytic) = -1.06369782240256 y[1] (numeric) = -1.06369782240256 absolute error = 2.220446049250313e-16 relative error = 2.087478231585566e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.059 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.059 Order of pole (six term test) = 4.459e-13 TOP MAIN SOLVE Loop x[1] = -1.79 y[1] (analytic) = -1.0613292811188 y[1] (numeric) = -1.0613292811188 absolute error = 2.220446049250313e-16 relative error = 2.092136803113196e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.05 Order of pole (six term test) = 2.564e-12 TOP MAIN SOLVE Loop x[1] = -1.78 y[1] (analytic) = -1.058940484363072 y[1] (numeric) = -1.058940484363073 absolute error = 4.440892098500626e-16 relative error = 4.193712643984631e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.042 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.042 Order of pole (six term test) = 3.56e-13 TOP MAIN SOLVE Loop x[1] = -1.77 y[1] (analytic) = -1.056531198801675 y[1] (numeric) = -1.056531198801675 absolute error = 2.220446049250313e-16 relative error = 2.101637937212605e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.033 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.426 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.033 Order of pole (six term test) = 5.241e-12 TOP MAIN SOLVE Loop x[1] = -1.76 y[1] (analytic) = -1.054101188032619 y[1] (numeric) = -1.05410118803262 absolute error = 2.220446049250313e-16 relative error = 2.106482825804007e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.024 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.523 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.024 Order of pole (six term test) = 3.937e-12 TOP MAIN SOLVE Loop x[1] = -1.75 y[1] (analytic) = -1.051650212548374 y[1] (numeric) = -1.051650212548374 absolute error = 4.440892098500626e-16 relative error = 4.222784387348141e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.016 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.016 Order of pole (six term test) = 9.789e-13 TOP MAIN SOLVE Loop x[1] = -1.74 y[1] (analytic) = -1.04917802969851 y[1] (numeric) = -1.04917802969851 absolute error = 4.440892098500626e-16 relative error = 4.232734552949754e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.007 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.007 Order of pole (six term test) = 2.114e-12 TOP MAIN SOLVE Loop x[1] = -1.73 y[1] (analytic) = -1.046684393652281 y[1] (numeric) = -1.046684393652281 absolute error = 4.440892098500626e-16 relative error = 4.242818681001502e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.998 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.998 Order of pole (six term test) = 5.941e-14 TOP MAIN SOLVE Loop x[1] = -1.72 y[1] (analytic) = -1.044169055361146 y[1] (numeric) = -1.044169055361146 absolute error = 6.661338147750939e-16 relative error = 6.379559050854067e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.99 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.99 Order of pole (six term test) = 5.953e-13 TOP MAIN SOLVE Loop x[1] = -1.71 y[1] (analytic) = -1.041631762521281 y[1] (numeric) = -1.041631762521282 absolute error = 6.661338147750939e-16 relative error = 6.395098908684483e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.981 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.981 Order of pole (six term test) = -7.34e-13 TOP MAIN SOLVE Loop x[1] = -1.7 y[1] (analytic) = -1.039072259536091 y[1] (numeric) = -1.039072259536092 absolute error = 4.440892098500626e-16 relative error = 4.273901124531346e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.972 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.972 Order of pole (six term test) = -1.168e-12 TOP MAIN SOLVE Loop x[1] = -1.69 y[1] (analytic) = -1.036490287478756 y[1] (numeric) = -1.036490287478757 absolute error = 6.661338147750939e-16 relative error = 6.426821580696645e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.964 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.964 Order of pole (six term test) = -2.378e-12 TOP MAIN SOLVE Loop x[1] = -1.68 y[1] (analytic) = -1.033885584054851 y[1] (numeric) = -1.033885584054852 absolute error = 6.661338147750939e-16 relative error = 6.443012892805297e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.955 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.955 Order of pole (six term test) = -1.276e-12 TOP MAIN SOLVE Loop x[1] = -1.67 y[1] (analytic) = -1.031257883565058 y[1] (numeric) = -1.031257883565059 absolute error = 6.661338147750939e-16 relative error = 6.459430035795409e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.947 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.947 Order of pole (six term test) = -3.415e-12 TOP MAIN SOLVE Loop x[1] = -1.66 y[1] (analytic) = -1.028606916868018 y[1] (numeric) = -1.028606916868019 absolute error = 6.661338147750939e-16 relative error = 6.476077536046421e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.938 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.938 Order of pole (six term test) = -1.371e-12 TOP MAIN SOLVE Loop x[1] = -1.65 y[1] (analytic) = -1.025932411343353 y[1] (numeric) = -1.025932411343353 absolute error = 6.661338147750939e-16 relative error = 6.492960037229551e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.929 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.929 Order of pole (six term test) = -4.872e-12 TOP MAIN SOLVE Loop x[1] = -1.64 y[1] (analytic) = -1.023234090854899 y[1] (numeric) = -1.0232340908549 absolute error = 6.661338147750939e-16 relative error = 6.510082304026323e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.921 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.00393 Order of pole (three term test) = -1.421 Radius of convergence (six term test) for eq 1 = 1.921 Order of pole (six term test) = -3.35e-12 TOP MAIN SOLVE Loop x[1] = -1.63 y[1] (analytic) = -1.020511675714193 y[1] (numeric) = -1.020511675714194 absolute error = 6.661338147750939e-16 relative error = 6.52744922598664e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.912 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.009678 Order of pole (three term test) = -6.027 Radius of convergence (six term test) for eq 1 = 1.912 Order of pole (six term test) = -4.457e-12 TOP MAIN SOLVE Loop x[1] = -1.62 y[1] (analytic) = -1.017764882644256 y[1] (numeric) = -1.017764882644257 absolute error = 6.661338147750939e-16 relative error = 6.545065821532483e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.904 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01089 Order of pole (three term test) = -15.29 Radius of convergence (six term test) for eq 1 = 1.904 Order of pole (six term test) = -3.514e-12 TOP MAIN SOLVE Loop x[1] = -1.61 y[1] (analytic) = -1.014993424743717 y[1] (numeric) = -1.014993424743718 absolute error = 8.881784197001252e-16 relative error = 8.750582989484761e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.895 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.007497 Order of pole (three term test) = -28.74 Radius of convergence (six term test) for eq 1 = 1.895 Order of pole (six term test) = -5.185e-12 TOP MAIN SOLVE Loop x[1] = -1.6 y[1] (analytic) = -1.012197011451334 y[1] (numeric) = -1.012197011451335 absolute error = 6.661338147750939e-16 relative error = 6.581068776521687e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.887 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.887 Order of pole (six term test) = 8.336e-12 TOP MAIN SOLVE Loop x[1] = -1.59 y[1] (analytic) = -1.009375348510952 y[1] (numeric) = -1.009375348510953 absolute error = 6.661338147750939e-16 relative error = 6.59946585537071e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.878 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.878 Order of pole (six term test) = -1.966e-12 TOP MAIN SOLVE Loop x[1] = -1.58 y[1] (analytic) = -1.006528137936965 y[1] (numeric) = -1.006528137936965 absolute error = 6.661338147750939e-16 relative error = 6.618134055749681e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.87 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.87 Order of pole (six term test) = -9.077e-13 TOP MAIN SOLVE Loop x[1] = -1.57 y[1] (analytic) = -1.003655077980327 y[1] (numeric) = -1.003655077980328 absolute error = 6.661338147750939e-16 relative error = 6.637079106056703e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.861 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.861 Order of pole (six term test) = -1.84e-12 TOP MAIN SOLVE Loop x[1] = -1.56 y[1] (analytic) = -1.000755863095186 y[1] (numeric) = -1.000755863095187 absolute error = 6.661338147750939e-16 relative error = 6.656306891021781e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.853 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.853 Order of pole (six term test) = -2.192e-13 TOP MAIN SOLVE Loop x[1] = -1.55 y[1] (analytic) = -0.9978301839061904 y[1] (numeric) = -0.997830183906191 absolute error = 6.661338147750939e-16 relative error = 6.675823456927212e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.845 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 0.8208 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.845 Order of pole (six term test) = -1.841e-12 TOP MAIN SOLVE Loop x[1] = -1.54 y[1] (analytic) = -0.9948777271765434 y[1] (numeric) = -0.9948777271765442 absolute error = 7.771561172376096e-16 relative error = 7.811574186540225e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.836 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.836 Order of pole (six term test) = 6.619e-13 TOP MAIN SOLVE Loop x[1] = -1.53 y[1] (analytic) = -0.991898175776877 y[1] (numeric) = -0.9918981757768777 absolute error = 6.661338147750939e-16 relative error = 6.715747957227192e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.828 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.828 Order of pole (six term test) = 2.807e-13 TOP MAIN SOLVE Loop x[1] = -1.52 y[1] (analytic) = -0.9888912086550109 y[1] (numeric) = -0.9888912086550117 absolute error = 7.771561172376096e-16 relative error = 7.858863648860001e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.819 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.819 Order of pole (six term test) = 1.328e-12 TOP MAIN SOLVE Loop x[1] = -1.51 y[1] (analytic) = -0.9858565008066834 y[1] (numeric) = -0.9858565008066842 absolute error = 7.771561172376096e-16 relative error = 7.883055156624687e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.811 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.811 Order of pole (six term test) = 4.436e-13 Finished! diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ; Iterations = 50 Total Elapsed Time = 0 Seconds Elapsed Time(since restart) = 0 Seconds Time to Timeout = 3 Minutes 0 Seconds Percent Done = 102 %