##############ECHO OF PROBLEM################# ##############temp/sing2postode.ode################# diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=20; ! /* 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_type_given_pole=2; array_given_rad_poles[1][1]=0.0; array_given_rad_poles[1][2]=1.0; array_given_ord_poles[1][1]=1.0; 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=100000000; glob_max_minutes=10.0; 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 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 500000 step_error = 7.071067811865475e-15 est_needed_step_err = 7.071067811865475e-15 opt_iter = 1 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) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-10 range = 0.5 estimated_steps = 500000 step_error = 7.828723661341926e-15 est_needed_step_err = 7.828723661341926e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.450574160593344e-103 estimated_step_error = 1.450574160593344e-103 Double H and LOOP opt_iter = 2 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) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 10 estimated_h = 2e-06 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-10 range = 0.5 estimated_steps = 250000 step_error = 1.10714871779409e-14 est_needed_step_err = 1.10714871779409e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.506485024763502e-99 estimated_step_error = 9.506485024763502e-99 Double H and LOOP opt_iter = 3 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) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 10 estimated_h = 4e-06 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-10 range = 0.5 estimated_steps = 125000 step_error = 1.565744732268385e-14 est_needed_step_err = 1.565744732268385e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.230172917146513e-94 estimated_step_error = 6.230172917146513e-94 Double H and LOOP opt_iter = 4 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) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 10 estimated_h = 8e-06 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-10 range = 0.5 estimated_steps = 62500 step_error = 2.214297435588181e-14 est_needed_step_err = 2.214297435588181e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.083009912693051e-89 estimated_step_error = 4.083009912693051e-89 Double H and LOOP opt_iter = 5 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) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 10 estimated_h = 1.6e-05 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-10 range = 0.5 estimated_steps = 31250 step_error = 3.13148946453677e-14 est_needed_step_err = 3.13148946453677e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.675846343644817e-84 estimated_step_error = 2.675846343644817e-84 Double H and LOOP opt_iter = 6 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) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 10 estimated_h = 3.2e-05 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-10 range = 0.5 estimated_steps = 15625 step_error = 4.428594871176361e-14 est_needed_step_err = 4.428594871176361e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.75364917049021e-79 estimated_step_error = 1.75364917049021e-79 Double H and LOOP opt_iter = 7 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) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 10 estimated_h = 6.4e-05 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-10 range = 0.5 estimated_steps = 7812.5 step_error = 6.262978929073541e-14 est_needed_step_err = 6.262978929073541e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.149280054178546e-74 estimated_step_error = 1.149280054178546e-74 Double H and LOOP opt_iter = 8 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) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 10 estimated_h = 0.000128 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-10 range = 0.5 estimated_steps = 3906.25 step_error = 8.857189742352723e-14 est_needed_step_err = 8.857189742352723e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.532033619367497e-70 estimated_step_error = 7.532033619367497e-70 Double H and LOOP opt_iter = 9 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) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 10 estimated_h = 0.000256 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-10 range = 0.5 estimated_steps = 1953.125 step_error = 1.252595785814708e-13 est_needed_step_err = 1.252595785814708e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.93634017032486e-65 estimated_step_error = 4.93634017032486e-65 Double H and LOOP opt_iter = 10 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) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 10 estimated_h = 0.000512 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-10 range = 0.5 estimated_steps = 976.5625 step_error = 1.771437948470545e-13 est_needed_step_err = 1.771437948470545e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.235272082305514e-60 estimated_step_error = 3.235272082305514e-60 Double H and LOOP opt_iter = 11 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) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 10 estimated_h = 0.001024 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-10 range = 0.5 estimated_steps = 488.28125 step_error = 2.505191571629416e-13 est_needed_step_err = 2.505191571629416e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.120519852918538e-55 estimated_step_error = 2.120519852918538e-55 Double H and LOOP opt_iter = 12 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) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 10 estimated_h = 0.002048 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-10 range = 0.5 estimated_steps = 244.140625 step_error = 3.542875896941089e-13 est_needed_step_err = 3.542875896941089e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.390034209479254e-50 estimated_step_error = 1.390034209479254e-50 Double H and LOOP opt_iter = 13 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) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 10 estimated_h = 0.004096 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-10 range = 0.5 estimated_steps = 122.0703125 step_error = 5.010383143258833e-13 est_needed_step_err = 5.010383143258833e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.114060226246165e-46 estimated_step_error = 9.114060226246165e-46 Double H and LOOP opt_iter = 14 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) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 10 estimated_h = 0.008192 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-10 range = 0.5 estimated_steps = 61.03515625 step_error = 7.085751793882178e-13 est_needed_step_err = 7.085751793882178e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.978675092256558e-41 estimated_step_error = 5.978675092256558e-41 Double H and LOOP opt_iter = 15 SETTING H FOR DISPLAY INTERVAL 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 = 1.365 Order of pole (six term test) = -2.576e-14 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 % Desired digits = 10 Estimated correct digits = 13 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) = -1.954e-14 TOP MAIN SOLVE Loop x[1] = -1.99 y[1] (analytic) = -1.105140688364494 y[1] (numeric) = -1.105140688364494 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 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) = -1.652e-13 TOP MAIN SOLVE Loop x[1] = -1.98 y[1] (analytic) = -1.103116481582997 y[1] (numeric) = -1.103116481582997 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 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) = -1.545e-13 TOP MAIN SOLVE Loop x[1] = -1.97 y[1] (analytic) = -1.101075917953986 y[1] (numeric) = -1.101075917953986 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 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) = -9.148e-14 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 % Desired digits = 10 Estimated correct digits = 13 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) = -3.553e-14 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 % Desired digits = 10 Estimated correct digits = 12 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) = -3.464e-14 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 % Desired digits = 10 Estimated correct digits = 12 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) = -1.155e-14 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 % Desired digits = 10 Estimated correct digits = 12 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) = -6.573e-14 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 % Desired digits = 10 Estimated correct digits = 12 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 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.165 Order of pole (six term test) = -1.812e-13 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 % Desired digits = 10 Estimated correct digits = 12 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 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.156 Order of pole (six term test) = 8.082e-14 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 % Desired digits = 10 Estimated correct digits = 12 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 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.147 Order of pole (six term test) = -6.484e-14 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 % Desired digits = 10 Estimated correct digits = 12 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 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.138 Order of pole (six term test) = -9.859e-14 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 % Desired digits = 10 Estimated correct digits = 12 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) = -1.954e-14 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 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.121 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 = 2.121 Order of pole (six term test) = -6.306e-14 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 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.112 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 = 2.112 Order of pole (six term test) = -1.306e-13 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 % Desired digits = 10 Estimated correct digits = 12 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) = -9.681e-14 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 % Desired digits = 10 Estimated correct digits = 12 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) = -4.352e-14 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 % Desired digits = 10 Estimated correct digits = 12 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) = -6.128e-14 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 % Desired digits = 10 Estimated correct digits = 12 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) = -5.063e-14 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 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.068 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 = 2.068 Order of pole (six term test) = -8.26e-14 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 % Desired digits = 10 Estimated correct digits = 12 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) = 8.882e-16 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 % Desired digits = 10 Estimated correct digits = 12 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) = -2.842e-14 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 % Desired digits = 10 Estimated correct digits = 12 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) = 0 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 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.033 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 = 2.033 Order of pole (six term test) = -2.22e-14 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 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.024 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 = 2.024 Order of pole (six term test) = -6.128e-14 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 % Desired digits = 10 Estimated correct digits = 12 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) = -2.576e-14 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 % Desired digits = 10 Estimated correct digits = 12 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) = 1.155e-14 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 % Desired digits = 10 Estimated correct digits = 12 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) = 0 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 % Desired digits = 10 Estimated correct digits = 12 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) = 0 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 % Desired digits = 10 Estimated correct digits = 12 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) = -3.109e-14 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 % Desired digits = 10 Estimated correct digits = 12 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) = 6.217e-15 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 % Desired digits = 10 Estimated correct digits = 12 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) = -4.441e-15 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 % Desired digits = 10 Estimated correct digits = 12 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) = 1.776e-15 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 % Desired digits = 10 Estimated correct digits = 12 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) = 1.332e-14 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 % Desired digits = 10 Estimated correct digits = 12 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) = -1.776e-15 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 % Desired digits = 10 Estimated correct digits = 12 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) = 7.105e-15 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 % Desired digits = 10 Estimated correct digits = 12 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 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.921 Order of pole (six term test) = 0 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 % Desired digits = 10 Estimated correct digits = 12 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 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.912 Order of pole (six term test) = -1.776e-15 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 % Desired digits = 10 Estimated correct digits = 12 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 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.904 Order of pole (six term test) = 3.464e-14 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 % Desired digits = 10 Estimated correct digits = 12 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 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.895 Order of pole (six term test) = 8.882e-16 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 % Desired digits = 10 Estimated correct digits = 12 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) = 2.132e-14 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 % Desired digits = 10 Estimated correct digits = 12 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) = 1.776e-15 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 % Desired digits = 10 Estimated correct digits = 12 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) = 2.842e-14 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 % Desired digits = 10 Estimated correct digits = 12 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) = 2.753e-14 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 % Desired digits = 10 Estimated correct digits = 12 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) = 2.398e-14 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 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.845 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 = 1.845 Order of pole (six term test) = 1.954e-14 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 % Desired digits = 10 Estimated correct digits = 12 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) = -2.931e-14 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 % Desired digits = 10 Estimated correct digits = 12 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) = -1.776e-14 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 % Desired digits = 10 Estimated correct digits = 12 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) = 3.642e-14 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 % Desired digits = 10 Estimated correct digits = 12 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) = -2.665e-15 Finished! diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; Iterations = 50 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 102 %