##############ECHO OF PROBLEM################# ##############temp/sing6_backpostode.ode################# diff ( y , x , 1 ) = m1 * 2.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=30; max_terms=20; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=3.0; x_end=2.0; 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]=6.0; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=3.0; 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(1.0/ ( x - 6.0 ) / ( x - 6.0 )); } // 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 = -1 estimated_steps = 1000000 step_error = 5e-21 est_needed_step_err = 5e-21 opt_iter = 1 min_size = 0.1111111111111111 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -1 estimated_steps = 1000000 step_error = 5e-21 est_needed_step_err = 5e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.839701975293304e-105 estimated_step_error = 4.839701975293304e-105 Double H and LOOP opt_iter = 2 min_size = 0.1111111111111111 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -1 estimated_steps = 500000 step_error = 7.071067811865475e-21 est_needed_step_err = 7.071067811865475e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.171746588999422e-100 estimated_step_error = 3.171746588999422e-100 Double H and LOOP opt_iter = 3 min_size = 0.1111111111111111 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -1 estimated_steps = 250000 step_error = 9.999999999999999e-21 est_needed_step_err = 9.999999999999999e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.078635192446023e-95 estimated_step_error = 2.078635192446023e-95 Double H and LOOP opt_iter = 4 min_size = 0.1111111111111111 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -1 estimated_steps = 125000 step_error = 1.414213562373095e-20 est_needed_step_err = 1.414213562373095e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.36225350497467e-90 estimated_step_error = 1.36225350497467e-90 Double H and LOOP opt_iter = 5 min_size = 0.1111111111111111 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -1 estimated_steps = 62500 step_error = 2e-20 est_needed_step_err = 2e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.927653366886491e-86 estimated_step_error = 8.927653366886491e-86 Double H and LOOP opt_iter = 6 min_size = 0.1111111111111111 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -1 estimated_steps = 31250 step_error = 2.82842712474619e-20 est_needed_step_err = 2.82842712474619e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.850812226168499e-81 estimated_step_error = 5.850812226168499e-81 Double H and LOOP opt_iter = 7 min_size = 0.1111111111111111 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -1 estimated_steps = 15625 step_error = 4e-20 est_needed_step_err = 4e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.834369053610431e-76 estimated_step_error = 3.834369053610431e-76 Double H and LOOP opt_iter = 8 min_size = 0.1111111111111111 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -1 estimated_steps = 7812.5 step_error = 5.65685424949238e-20 est_needed_step_err = 5.65685424949238e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.51286687601747e-71 estimated_step_error = 2.51286687601747e-71 Double H and LOOP opt_iter = 9 min_size = 0.1111111111111111 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -1 estimated_steps = 3906.25 step_error = 8e-20 est_needed_step_err = 8e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.646799371389444e-66 estimated_step_error = 1.646799371389444e-66 Double H and LOOP opt_iter = 10 min_size = 0.1111111111111111 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -1 estimated_steps = 1953.125 step_error = 1.131370849898476e-19 est_needed_step_err = 1.131370849898476e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.07920310038136e-61 estimated_step_error = 1.07920310038136e-61 Double H and LOOP opt_iter = 11 min_size = 0.1111111111111111 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -1 estimated_steps = 976.5625 step_error = 1.6e-19 est_needed_step_err = 1.6e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.072097498250659e-57 estimated_step_error = 7.072097498250659e-57 Double H and LOOP opt_iter = 12 min_size = 0.1111111111111111 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -1 estimated_steps = 488.28125 step_error = 2.262741699796952e-19 est_needed_step_err = 2.262741699796952e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.634025585524804e-52 estimated_step_error = 4.634025585524804e-52 Double H and LOOP opt_iter = 13 min_size = 0.1111111111111111 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -1 estimated_steps = 244.140625 step_error = 3.2e-19 est_needed_step_err = 3.2e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.035980000758586e-47 estimated_step_error = 3.035980000758586e-47 Double H and LOOP opt_iter = 14 min_size = 0.1111111111111111 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -1 estimated_steps = 122.0703125 step_error = 4.525483399593904e-19 est_needed_step_err = 4.525483399593904e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.988383126485802e-42 estimated_step_error = 1.988383126485802e-42 Double H and LOOP opt_iter = 15 min_size = 0.1111111111111111 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -0.016384 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -1 estimated_steps = 61.03515625 step_error = 6.4e-19 est_needed_step_err = 6.4e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.301436562777215e-37 estimated_step_error = 1.301436562777215e-37 Double H and LOOP opt_iter = 16 min_size = 0.1111111111111111 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -0.032768 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -1 estimated_steps = 30.517578125 step_error = 9.050966799187808e-19 est_needed_step_err = 9.050966799187808e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.507287217999273e-33 estimated_step_error = 8.507287217999273e-33 Double H and LOOP opt_iter = 17 min_size = 0.1111111111111111 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -0.065536 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -1 estimated_steps = 15.2587890625 step_error = 1.28e-18 est_needed_step_err = 1.28e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.54697112876515e-28 estimated_step_error = 5.54697112876515e-28 Double H and LOOP opt_iter = 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL START of Soultion TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (closed_form) = 0.1040582726326743 y[1] (numeric) = 0.1040582723458603 absolute error = 2.868139614697895e-10 relative error = 2.756282169724678e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = -0.1 Radius of convergence (given) for eq 1 = 3.1 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.1 Order of pole (three term test) = 2.491e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (closed_form) = 0.09765625 y[1] (numeric) = 0.0976562494921224 absolute error = 5.078776010858377e-10 relative error = 5.200666635118978e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = -0.1 Radius of convergence (given) for eq 1 = 3.2 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (closed_form) = 0.09182736455463726 y[1] (numeric) = 0.09182736387496891 absolute error = 6.796683493792699e-10 relative error = 7.401588324740251e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = -0.1 Radius of convergence (given) for eq 1 = 3.3 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.3 Order of pole (three term test) = 8.127e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (closed_form) = 0.08650519031141866 y[1] (numeric) = 0.08650518949721703 absolute error = 8.142016366674554e-10 relative error = 9.412170919875786e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = -0.1 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (closed_form) = 0.08163265306122447 y[1] (numeric) = 0.08163265214090006 absolute error = 9.203244138999978e-10 relative error = 1.127397407027497e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = -0.1 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.5 Order of pole (three term test) = 5.936e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.399999999999999 y[1] (closed_form) = 0.07716049382716048 y[1] (numeric) = 0.07716049282255018 absolute error = 1.004610297727915e-09 relative error = 1.301974945855378e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = -0.1 Radius of convergence (given) for eq 1 = 3.6 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.6 Order of pole (three term test) = 3.455e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.299999999999999 y[1] (closed_form) = 0.07304601899196492 y[1] (numeric) = 0.07304601791997908 absolute error = 1.071985833434042e-09 relative error = 1.467548605971203e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = -0.1 Radius of convergence (given) for eq 1 = 3.7 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.7 Order of pole (three term test) = 7.86e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.199999999999999 y[1] (closed_form) = 0.06925207756232683 y[1] (numeric) = 0.06925207643615361 absolute error = 1.126173224119675e-09 relative error = 1.626194135628812e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = -0.1 Radius of convergence (given) for eq 1 = 3.8 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.8 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.099999999999999 y[1] (closed_form) = 0.06574621959237341 y[1] (numeric) = 0.06574621842236704 absolute error = 1.170006369566323e-09 relative error = 1.779579688110378e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = -0.1 Radius of convergence (given) for eq 1 = 3.9 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.9 Order of pole (three term test) = 4.767e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; Iterations = 10 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Expected Time Remaining = 0.0 Seconds Optimized Time Remaining = 0.0 Seconds Expected Total Time = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 0 %