##############ECHO OF PROBLEM################# ##############temp/sing7_backpostode.ode################# diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=64; max_terms=30; ! // 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; // 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 )/ ( x - 6.0 )/ ( 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 = 3.333333333333333e-21 est_needed_step_err = 3.333333333333333e-21 opt_iter = 1 min_size = 0.004115226337448559 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 = 3.333333333333333e-21 est_needed_step_err = 3.333333333333333e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.922909014320238e-170 estimated_step_error = 3.922909014320238e-170 Double H and LOOP opt_iter = 2 min_size = 0.004115226337448559 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 = 4.714045207910316e-21 est_needed_step_err = 4.714045207910316e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.632619252744838e-162 estimated_step_error = 2.632619252744838e-162 Double H and LOOP opt_iter = 3 min_size = 0.004115226337448559 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 = 6.666666666666667e-21 est_needed_step_err = 6.666666666666667e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.766720306867125e-154 estimated_step_error = 1.766720306867125e-154 Double H and LOOP opt_iter = 4 min_size = 0.004115226337448559 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 = 9.428090415820633e-21 est_needed_step_err = 9.428090415820633e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.18562516685425e-146 estimated_step_error = 1.18562516685425e-146 Double H and LOOP opt_iter = 5 min_size = 0.004115226337448559 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 = 1.333333333333333e-20 est_needed_step_err = 1.333333333333333e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.956585591890105e-139 estimated_step_error = 7.956585591890105e-139 Double H and LOOP opt_iter = 6 min_size = 0.004115226337448559 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 = 1.885618083164127e-20 est_needed_step_err = 1.885618083164127e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.339560492476499e-131 estimated_step_error = 5.339560492476499e-131 Double H and LOOP opt_iter = 7 min_size = 0.004115226337448559 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 = 2.666666666666667e-20 est_needed_step_err = 2.666666666666667e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.583299986067772e-123 estimated_step_error = 3.583299986067772e-123 Double H and LOOP opt_iter = 8 min_size = 0.004115226337448559 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 = 3.771236166328253e-20 est_needed_step_err = 3.771236166328253e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.404687214619923e-115 estimated_step_error = 2.404687214619923e-115 Double H and LOOP opt_iter = 9 min_size = 0.004115226337448559 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 = 5.333333333333333e-20 est_needed_step_err = 5.333333333333333e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.613725122074629e-107 estimated_step_error = 1.613725122074629e-107 Double H and LOOP opt_iter = 10 min_size = 0.004115226337448559 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 = 7.542472332656506e-20 est_needed_step_err = 7.542472332656506e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.082908106525385e-99 estimated_step_error = 1.082908106525385e-99 Double H and LOOP opt_iter = 11 min_size = 0.004115226337448559 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 = 1.066666666666667e-19 est_needed_step_err = 1.066666666666667e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.266676210378411e-92 estimated_step_error = 7.266676210378411e-92 Double H and LOOP opt_iter = 12 min_size = 0.004115226337448559 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 = 1.508494466531301e-19 est_needed_step_err = 1.508494466531301e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.875782673742115e-84 estimated_step_error = 4.875782673742115e-84 Double H and LOOP opt_iter = 13 min_size = 0.004115226337448559 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 = 2.133333333333333e-19 est_needed_step_err = 2.133333333333333e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.271007566269152e-76 estimated_step_error = 3.271007566269152e-76 Double H and LOOP opt_iter = 14 min_size = 0.004115226337448559 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 = 3.016988933062603e-19 est_needed_step_err = 3.016988933062603e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.193694873261646e-68 estimated_step_error = 2.193694873261646e-68 Double H and LOOP opt_iter = 15 min_size = 0.004115226337448559 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 = 4.266666666666667e-19 est_needed_step_err = 4.266666666666667e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.470233245702015e-60 estimated_step_error = 1.470233245702015e-60 Double H and LOOP opt_iter = 16 min_size = 0.004115226337448559 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 = 6.033977866125205e-19 est_needed_step_err = 6.033977866125205e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.84075984717572e-53 estimated_step_error = 9.84075984717572e-53 Double H and LOOP opt_iter = 17 min_size = 0.004115226337448559 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 = 8.533333333333333e-19 est_needed_step_err = 8.533333333333333e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.569653339824282e-45 estimated_step_error = 6.569653339824282e-45 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) = -0.003492943259127732 y[1] (numeric) = -0.003492942709077674 absolute error = 5.500500580186973e-10 relative error = 1.574746616857605e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = -0.1 Radius of convergence (given) for eq 1 = 3.1 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.1 Order of pole (three term test) = 1.724e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (closed_form) = -0.002980232238769531 y[1] (numeric) = -0.002980231304318123 absolute error = 9.344514086129241e-10 relative error = 3.135498624760658e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = -0.1 Radius of convergence (given) for eq 1 = 3.2 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.2 Order of pole (three term test) = 1.275e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (closed_form) = -0.00255523178213644 y[1] (numeric) = -0.002555230575992177 absolute error = 1.20614426259158e-09 relative error = 4.72029297312167e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = -0.1 Radius of convergence (given) for eq 1 = 3.3 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.3 Order of pole (three term test) = 8.928e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (closed_form) = -0.002200925867886695 y[1] (numeric) = -0.002200924467662047 absolute error = 1.400224647601228e-09 relative error = 6.361980055901241e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = -0.1 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.4 Order of pole (three term test) = 1.188e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (closed_form) = -0.001903968584518354 y[1] (numeric) = -0.001903967044263593 absolute error = 1.540254761624518e-09 relative error = 8.08970680581978e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = -0.1 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.5 Order of pole (three term test) = 1.505e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.399999999999999 y[1] (closed_form) = -0.001653817168792019 y[1] (numeric) = -0.001653815526549614 absolute error = 1.642242404781627e-09 relative error = 9.930011828218918e-05 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 7 h = -0.1 Radius of convergence (given) for eq 1 = 3.6 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.6 Order of pole (three term test) = 1.823e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.299999999999999 y[1] (closed_form) = -0.001442086727182297 y[1] (numeric) = -0.001442085009996912 absolute error = 1.717185384554967e-09 relative error = 0.0001190764294676082 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 6 h = -0.1 Radius of convergence (given) for eq 1 = 3.7 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.199999999999999 y[1] (closed_form) = -0.001262065854394351 y[1] (numeric) = -0.00126206408167466 absolute error = 1.772719690224661e-09 relative error = 0.0001404617424718591 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 6 h = -0.1 Radius of convergence (given) for eq 1 = 3.8 Order of pole (given) = 0 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) = -0.00110835010017656 y[1] (numeric) = -0.001108348285976256 absolute error = 1.814200304307151e-09 relative error = 0.0001636847692816691 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 6 h = -0.1 Radius of convergence (given) for eq 1 = 3.9 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.9 Order of pole (three term test) = 1.26e-13 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( 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 %