##############ECHO OF PROBLEM################# ##############temp/sing5postode.ode################# diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=20; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=-1.0; x_end=-0.7; 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]=0.0; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=4.0; 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/x/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 = 0.3 estimated_steps = 300000.0000000001 step_error = 9.128709291752767e-21 est_needed_step_err = 9.128709291752767e-21 opt_iter = 1 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.3 estimated_steps = 300000.0000000001 step_error = 9.128709291752767e-21 est_needed_step_err = 9.128709291752767e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.562503088236751e-96 estimated_step_error = 6.562503088236751e-96 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.3 estimated_steps = 150000 step_error = 1.290994448735805e-20 est_needed_step_err = 1.290994448735805e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.300804047815587e-91 estimated_step_error = 4.300804047815587e-91 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.3 estimated_steps = 75000.00000000001 step_error = 1.825741858350553e-20 est_needed_step_err = 1.825741858350553e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.818577593557857e-86 estimated_step_error = 2.818577593557857e-86 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.3 estimated_steps = 37500.00000000001 step_error = 2.581988897471611e-20 est_needed_step_err = 2.581988897471611e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.84718648877761e-81 estimated_step_error = 1.84718648877761e-81 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.3 estimated_steps = 18750 step_error = 3.651483716701107e-20 est_needed_step_err = 3.651483716701107e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.210576694767835e-76 estimated_step_error = 1.210576694767835e-76 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.3 estimated_steps = 9375.000000000002 step_error = 5.163977794943221e-20 est_needed_step_err = 5.163977794943221e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.93369516334265e-72 estimated_step_error = 7.93369516334265e-72 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.3 estimated_steps = 4687.500000000001 step_error = 7.302967433402214e-20 est_needed_step_err = 7.302967433402214e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.199504761864271e-67 estimated_step_error = 5.199504761864271e-67 Double H and LOOP opt_iter = 8 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.3 estimated_steps = 2343.75 step_error = 1.032795558988644e-19 est_needed_step_err = 1.032795558988644e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.407650074260886e-62 estimated_step_error = 3.407650074260886e-62 Double H and LOOP opt_iter = 9 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.3 estimated_steps = 1171.875 step_error = 1.460593486680443e-19 est_needed_step_err = 1.460593486680443e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.233372088680488e-57 estimated_step_error = 2.233372088680488e-57 Double H and LOOP opt_iter = 10 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.3 estimated_steps = 585.9375000000001 step_error = 2.065591117977288e-19 est_needed_step_err = 2.065591117977288e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.463839103064355e-52 estimated_step_error = 1.463839103064355e-52 Double H and LOOP opt_iter = 11 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.3 estimated_steps = 292.9687500000001 step_error = 2.921186973360886e-19 est_needed_step_err = 2.921186973360886e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.595728514958766e-48 estimated_step_error = 9.595728514958766e-48 Double H and LOOP opt_iter = 12 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.3 estimated_steps = 146.484375 step_error = 4.131182235954577e-19 est_needed_step_err = 4.131182235954577e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.291689970870765e-43 estimated_step_error = 6.291689970870765e-43 Double H and LOOP opt_iter = 13 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.3 estimated_steps = 73.24218750000001 step_error = 5.842373946721771e-19 est_needed_step_err = 5.842373946721771e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.127303566141865e-38 estimated_step_error = 4.127303566141865e-38 Double H and LOOP opt_iter = 14 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.3 estimated_steps = 36.62109375000001 step_error = 8.262364471909154e-19 est_needed_step_err = 8.262364471909154e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.710103663121732e-33 estimated_step_error = 2.710103663121732e-33 Double H and LOOP opt_iter = 15 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.3 estimated_steps = 18.310546875 step_error = 1.168474789344354e-18 est_needed_step_err = 1.168474789344354e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.782993957434995e-28 estimated_step_error = 1.782993957434995e-28 Double H and LOOP opt_iter = 16 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9155 Order of pole (three term test) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = -1 y[1] (closed_form) = -1 y[1] (numeric) = -1 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.03000000000000001 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 3.72e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.97 y[1] (closed_form) = -1.095682681529968 y[1] (numeric) = -1.095682673394397 absolute error = 8.135570217504551e-09 relative error = 7.42511527712053e-07 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 9 h = 0.03000000000000001 Radius of convergence (given) for eq 1 = 0.97 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.97 Order of pole (three term test) = 8.421e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9399999999999999 y[1] (closed_form) = -1.203972144900456 y[1] (numeric) = -1.203972126042916 absolute error = 1.885753930785938e-08 relative error = 1.566277042847908e-06 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 8 h = 0.03000000000000001 Radius of convergence (given) for eq 1 = 0.94 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.94 Order of pole (three term test) = 4.108e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9099999999999999 y[1] (closed_form) = -1.327014972709937 y[1] (numeric) = -1.327014939597777 absolute error = 3.311216079104895e-08 relative error = 2.495236411947154e-06 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 8 h = 0.03000000000000001 Radius of convergence (given) for eq 1 = 0.91 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.91 Order of pole (three term test) = 5.821e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8799999999999999 y[1] (closed_form) = -1.467411720510895 y[1] (numeric) = -1.467411668270296 absolute error = 5.224059829167516e-08 relative error = 3.560050499902444e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.03000000000000001 Radius of convergence (given) for eq 1 = 0.88 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.88 Order of pole (three term test) = 7.964e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8499999999999999 y[1] (closed_form) = -1.628332994097294 y[1] (numeric) = -1.628332915931664 absolute error = 7.816562996865173e-08 relative error = 4.800346750449822e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.03000000000000001 Radius of convergence (given) for eq 1 = 0.85 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.85 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8199999999999998 y[1] (closed_form) = -1.813670724452635 y[1] (numeric) = -1.813670610774847 absolute error = 1.136777885157869e-07 relative error = 6.267829489837237e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.03000000000000001 Radius of convergence (given) for eq 1 = 0.82 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.82 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7899999999999998 y[1] (closed_form) = -2.028237117144893 y[1] (numeric) = -2.028236954264547 absolute error = 1.628803460995698e-07 relative error = 8.030636296058573e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.03000000000000001 Radius of convergence (given) for eq 1 = 0.79 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.79 Order of pole (three term test) = 4.035e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7599999999999998 y[1] (closed_form) = -2.278028867181807 y[1] (numeric) = -2.278028635289597 absolute error = 2.318922098787368e-07 relative error = 1.017951147237283e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.03000000000000001 Radius of convergence (given) for eq 1 = 0.76 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.76 Order of pole (three term test) = 4.676e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7299999999999998 y[1] (closed_form) = -2.570581748355473 y[1] (numeric) = -2.570581418378468 absolute error = 3.299770048315054e-07 relative error = 1.283666644885376e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.03000000000000001 Radius of convergence (given) for eq 1 = 0.73 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.73 Order of pole (three term test) = 5.156e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ; Iterations = 10 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 110 %