##############ECHO OF PROBLEM################# ##############temp/nonlinear2postode.ode################# diff ( y , x , 1 ) = y * y ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=20; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.0; x_end=0.2; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=1; array_given_rad_poles[1][1]=0.5; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=0.0; array_given_ord_poles[1][2]=0.0; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=16; glob_max_minutes=3.0; glob_subiter_method=3; glob_max_iter=100000000; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(2.0/(1.0 - 2.0*x)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.2 estimated_steps = 200000 step_error = 1.118033988749895e-20 est_needed_step_err = 1.118033988749895e-20 opt_iter = 1 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 0.2 estimated_steps = 200000 step_error = 2.23606797749979e-20 est_needed_step_err = 2.23606797749979e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.310721310721311e-91 estimated_step_error = 1.310721310721311e-91 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 0.2 estimated_steps = 100000 step_error = 3.162277660168379e-20 est_needed_step_err = 3.162277660168379e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.589951771903542e-87 estimated_step_error = 8.589951771903542e-87 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 0.2 estimated_steps = 50000.00000000001 step_error = 4.472135954999579e-20 est_needed_step_err = 4.472135954999579e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.629522052301328e-82 estimated_step_error = 5.629522052301328e-82 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 0.2 estimated_steps = 25000 step_error = 6.324555320336758e-20 est_needed_step_err = 6.324555320336758e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.689378329768548e-77 estimated_step_error = 3.689378329768548e-77 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 0.2 estimated_steps = 12500 step_error = 8.944271909999158e-20 est_needed_step_err = 8.944271909999158e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.417890325474466e-72 estimated_step_error = 2.417890325474466e-72 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 0.2 estimated_steps = 6250.000000000001 step_error = 1.264911064067352e-19 est_needed_step_err = 1.264911064067352e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.584613957931941e-67 estimated_step_error = 1.584613957931941e-67 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 0.2 estimated_steps = 3125 step_error = 1.788854381999832e-19 est_needed_step_err = 1.788854381999832e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.038525837360556e-62 estimated_step_error = 1.038525837360556e-62 Double H and LOOP opt_iter = 8 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 0.2 estimated_steps = 1562.5 step_error = 2.529822128134703e-19 est_needed_step_err = 2.529822128134703e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.806518572796085e-58 estimated_step_error = 6.806518572796085e-58 Double H and LOOP opt_iter = 9 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 0.2 estimated_steps = 781.2500000000001 step_error = 3.577708763999663e-19 est_needed_step_err = 3.577708763999663e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.461291130235445e-53 estimated_step_error = 4.461291130235445e-53 Double H and LOOP opt_iter = 10 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 0.2 estimated_steps = 390.6250000000001 step_error = 5.059644256269407e-19 est_needed_step_err = 5.059644256269407e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.924500618978521e-48 estimated_step_error = 2.924500618978521e-48 Double H and LOOP opt_iter = 11 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 0.2 estimated_steps = 195.3125 step_error = 7.155417527999327e-19 est_needed_step_err = 7.155417527999327e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.917583031104105e-43 estimated_step_error = 1.917583031104105e-43 Double H and LOOP opt_iter = 12 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 0.2 estimated_steps = 97.65625000000001 step_error = 1.011928851253881e-18 est_needed_step_err = 1.011928851253881e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.257996724346713e-38 estimated_step_error = 1.257996724346713e-38 Double H and LOOP opt_iter = 13 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 0.2 estimated_steps = 48.82812500000001 step_error = 1.431083505599865e-18 est_needed_step_err = 1.431083505599865e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.261361320257963e-34 estimated_step_error = 8.261361320257963e-34 Double H and LOOP opt_iter = 14 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 0.2 estimated_steps = 24.4140625 step_error = 2.023857702507763e-18 est_needed_step_err = 2.023857702507763e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.436525324605938e-29 estimated_step_error = 5.436525324605938e-29 Double H and LOOP opt_iter = 15 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 0.2 estimated_steps = 12.20703125 step_error = 2.862167011199731e-18 est_needed_step_err = 2.862167011199731e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.592554284321596e-24 estimated_step_error = 3.592554284321596e-24 Double H and LOOP opt_iter = 16 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3052 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.3052 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (closed_form) = 2 y[1] (numeric) = 2 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.02 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.02 y[1] (closed_form) = 2.083333333333333 y[1] (numeric) = 2.083333333333333 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.02 Radius of convergence (given) for eq 1 = 0.48 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.48 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.48 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.04 y[1] (closed_form) = 2.173913043478261 y[1] (numeric) = 2.173913043478261 absolute error = 4.440892098500626e-16 relative error = 2.042810365310288e-14 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.02 Radius of convergence (given) for eq 1 = 0.46 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.46 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.46 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.06 y[1] (closed_form) = 2.272727272727273 y[1] (numeric) = 2.272727272727273 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.02 Radius of convergence (given) for eq 1 = 0.44 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.44 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.44 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.08 y[1] (closed_form) = 2.380952380952381 y[1] (numeric) = 2.380952380952381 absolute error = 4.440892098500626e-16 relative error = 1.865174681370263e-14 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.02 Radius of convergence (given) for eq 1 = 0.42 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.42 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.42 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 2.5 y[1] (numeric) = 2.5 absolute error = 4.440892098500626e-16 relative error = 1.77635683940025e-14 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.02 Radius of convergence (given) for eq 1 = 0.4 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.4 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (closed_form) = 2.631578947368421 y[1] (numeric) = 2.631578947368422 absolute error = 4.440892098500626e-16 relative error = 1.687538997430238e-14 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.02 Radius of convergence (given) for eq 1 = 0.38 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.38 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.38 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (closed_form) = 2.777777777777778 y[1] (numeric) = 2.777777777777779 absolute error = 8.881784197001252e-16 relative error = 3.197442310920451e-14 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.02 Radius of convergence (given) for eq 1 = 0.36 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.36 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.36 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (closed_form) = 2.941176470588236 y[1] (numeric) = 2.941176470588236 absolute error = 8.881784197001252e-16 relative error = 3.019806626980426e-14 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.02 Radius of convergence (given) for eq 1 = 0.34 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.34 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.34 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (closed_form) = 3.125 y[1] (numeric) = 3.125000000000001 absolute error = 1.332267629550188e-15 relative error = 4.263256414560601e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.02 Radius of convergence (given) for eq 1 = 0.32 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.32 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.32 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (closed_form) = 3.333333333333333 y[1] (numeric) = 3.333333333333335 absolute error = 1.77635683940025e-15 relative error = 5.329070518200752e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.02 Radius of convergence (given) for eq 1 = 0.3 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.3 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = y * y ; Iterations = 11 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 120 %