##############ECHO OF PROBLEM################# ##############temp/sing3_backpostode.ode################# diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=20; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-0.7; 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]=0.0; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=2.0; 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); } /* 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 = -1.3 estimated_steps = 1300000 step_error = 4.385290096535146e-21 est_needed_step_err = 4.385290096535146e-21 opt_iter = 1 min_size = 2.040816326530612 glob_desired_digits_correct = 16 estimated_h = -1e-06 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-16 range = -1.3 estimated_steps = 1300000 step_error = 8.94957162558193e-21 est_needed_step_err = 8.94957162558193e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.151426604336032e-93 estimated_step_error = 1.151426604336032e-93 Double H and LOOP opt_iter = 2 min_size = 2.040816326530612 glob_desired_digits_correct = 16 estimated_h = -2e-06 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-16 range = -1.3 estimated_steps = 650000 step_error = 1.26566055703274e-20 est_needed_step_err = 1.26566055703274e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.545984321249431e-89 estimated_step_error = 7.545984321249431e-89 Double H and LOOP opt_iter = 3 min_size = 2.040816326530612 glob_desired_digits_correct = 16 estimated_h = -4e-06 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-16 range = -1.3 estimated_steps = 325000 step_error = 1.789914325116386e-20 est_needed_step_err = 1.789914325116386e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.945329635600357e-84 estimated_step_error = 4.945329635600357e-84 Double H and LOOP opt_iter = 4 min_size = 2.040816326530612 glob_desired_digits_correct = 16 estimated_h = -8e-06 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-16 range = -1.3 estimated_steps = 162500 step_error = 2.531321114065479e-20 est_needed_step_err = 2.531321114065479e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.240962514817413e-79 estimated_step_error = 3.240962514817413e-79 Double H and LOOP opt_iter = 5 min_size = 2.040816326530612 glob_desired_digits_correct = 16 estimated_h = -1.6e-05 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-16 range = -1.3 estimated_steps = 81250 step_error = 3.579828650232772e-20 est_needed_step_err = 3.579828650232772e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.123985770656064e-74 estimated_step_error = 2.123985770656064e-74 Double H and LOOP opt_iter = 6 min_size = 2.040816326530612 glob_desired_digits_correct = 16 estimated_h = -3.2e-05 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-16 range = -1.3 estimated_steps = 40625 step_error = 5.062642228130958e-20 est_needed_step_err = 5.062642228130958e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.391960342473341e-69 estimated_step_error = 1.391960342473341e-69 Double H and LOOP opt_iter = 7 min_size = 2.040816326530612 glob_desired_digits_correct = 16 estimated_h = -6.4e-05 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-16 range = -1.3 estimated_steps = 20312.5 step_error = 7.159657300465544e-20 est_needed_step_err = 7.159657300465544e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.122155063379819e-65 estimated_step_error = 9.122155063379819e-65 Double H and LOOP opt_iter = 8 min_size = 2.040816326530612 glob_desired_digits_correct = 16 estimated_h = -0.000128 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-16 range = -1.3 estimated_steps = 10156.25 step_error = 1.012528445626192e-19 est_needed_step_err = 1.012528445626192e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.97803834716196e-60 estimated_step_error = 5.97803834716196e-60 Double H and LOOP opt_iter = 9 min_size = 2.040816326530612 glob_desired_digits_correct = 16 estimated_h = -0.000256 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-16 range = -1.3 estimated_steps = 5078.125 step_error = 1.431931460093109e-19 est_needed_step_err = 1.431931460093109e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.917430143993059e-55 estimated_step_error = 3.917430143993059e-55 Double H and LOOP opt_iter = 10 min_size = 2.040816326530612 glob_desired_digits_correct = 16 estimated_h = -0.000512 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-16 range = -1.3 estimated_steps = 2539.0625 step_error = 2.025056891252383e-19 est_needed_step_err = 2.025056891252383e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.566885332850637e-50 estimated_step_error = 2.566885332850637e-50 Double H and LOOP opt_iter = 11 min_size = 2.040816326530612 glob_desired_digits_correct = 16 estimated_h = -0.001024 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-16 range = -1.3 estimated_steps = 1269.53125 step_error = 2.863862920186218e-19 est_needed_step_err = 2.863862920186218e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.681655344378907e-45 estimated_step_error = 1.681655344378907e-45 Double H and LOOP opt_iter = 12 min_size = 2.040816326530612 glob_desired_digits_correct = 16 estimated_h = -0.002048 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-16 range = -1.3 estimated_steps = 634.765625 step_error = 4.050113782504767e-19 est_needed_step_err = 4.050113782504767e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.10133201281393e-40 estimated_step_error = 1.10133201281393e-40 Double H and LOOP opt_iter = 13 min_size = 2.040816326530612 glob_desired_digits_correct = 16 estimated_h = -0.004096 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-16 range = -1.3 estimated_steps = 317.3828125 step_error = 5.727725840372435e-19 est_needed_step_err = 5.727725840372435e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.207779545357236e-36 estimated_step_error = 7.207779545357236e-36 Double H and LOOP opt_iter = 14 min_size = 2.040816326530612 glob_desired_digits_correct = 16 estimated_h = -0.008192 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-16 range = -1.3 estimated_steps = 158.69140625 step_error = 8.100227565009533e-19 est_needed_step_err = 8.100227565009533e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.710754790217147e-31 estimated_step_error = 4.710754790217147e-31 Double H and LOOP opt_iter = 15 min_size = 2.040816326530612 glob_desired_digits_correct = 16 estimated_h = -0.016384 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-16 range = -1.3 estimated_steps = 79.345703125 step_error = 1.145545168074487e-18 est_needed_step_err = 1.145545168074487e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.070424259303141e-26 estimated_step_error = 3.070424259303141e-26 Double H and LOOP opt_iter = 16 min_size = 2.040816326530612 glob_desired_digits_correct = 16 estimated_h = -0.032768 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-16 range = -1.3 estimated_steps = 39.6728515625 step_error = 1.620045513001907e-18 est_needed_step_err = 1.620045513001907e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.990549258647485e-21 estimated_step_error = 1.990549258647485e-21 Double H and LOOP opt_iter = 17 min_size = 2.040816326530612 glob_desired_digits_correct = 16 estimated_h = -0.065536 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-16 range = -1.3 estimated_steps = 19.83642578125 step_error = 2.291090336148974e-18 est_needed_step_err = 2.291090336148974e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.277003013991022e-16 estimated_step_error = 1.277003013991022e-16 Found H for OPTIMAL START of Soultion TOP MAIN SOLVE Loop x[1] = -0.732768 y[1] (closed_form) = 1.862374468237202 y[1] (numeric) = 1.862374428789553 absolute error = 3.944764892516162e-08 relative error = 2.118137334781018e-06 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 8 h = -0.032768 Radius of convergence (given) for eq 1 = 0.7328 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7328 Order of pole (three term test) = 3.346e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8638400000000001 y[1] (closed_form) = 1.340088189724308 y[1] (numeric) = 1.340088079346144 absolute error = 1.103781639422152e-07 relative error = 8.236634334112215e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = -0.032768 Radius of convergence (given) for eq 1 = 0.8638 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8638 Order of pole (three term test) = 7.283e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9949120000000001 y[1] (closed_form) = 1.010254193470823 y[1] (numeric) = 1.01025406275714 absolute error = 1.307136829886701e-07 relative error = 1.2938692443294e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = -0.032768 Radius of convergence (given) for eq 1 = 0.9949 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9949 Order of pole (three term test) = 7.882e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.125984 y[1] (closed_form) = 0.788743078809519 y[1] (numeric) = 0.7887429411783439 absolute error = 1.376311751233317e-07 relative error = 1.744943046994008e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = -0.032768 Radius of convergence (given) for eq 1 = 1.126 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.126 Order of pole (three term test) = 2.523e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.224288 y[1] (closed_form) = 0.6671643236859892 y[1] (numeric) = 0.6671641838435699 absolute error = 1.39842419311087e-07 relative error = 2.096071602547289e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = -0.032768 Radius of convergence (given) for eq 1 = 1.224 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.224 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.355359999999999 y[1] (closed_form) = 0.5443655976215902 y[1] (numeric) = 0.5443654563724056 absolute error = 1.412491845709241e-07 relative error = 2.594748551121922e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = -0.032768 Radius of convergence (given) for eq 1 = 1.355 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.355 Order of pole (three term test) = 5.133e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.486431999999999 y[1] (closed_form) = 0.4525951622028792 y[1] (numeric) = 0.4525950203117714 absolute error = 1.418911078077123e-07 relative error = 3.135055777377234e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = -0.032768 Radius of convergence (given) for eq 1 = 1.486 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.486 Order of pole (three term test) = 5.116e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.617503999999998 y[1] (closed_form) = 0.3822163609914455 y[1] (numeric) = 0.3822162187860234 absolute error = 1.422054221600355e-07 relative error = 3.720547749216268e-05 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 7 h = -0.032768 Radius of convergence (given) for eq 1 = 1.618 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.618 Order of pole (three term test) = 4.035e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.748575999999998 y[1] (closed_form) = 0.3270626668152107 y[1] (numeric) = 0.3270625244465621 absolute error = 1.423686485924058e-07 relative error = 4.352947096613862e-05 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 7 h = -0.032768 Radius of convergence (given) for eq 1 = 1.749 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.749 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.879647999999998 y[1] (closed_form) = 0.2830394333638326 y[1] (numeric) = 0.2830392909060884 absolute error = 1.424577442676878e-07 relative error = 5.033141233171056e-05 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 7 h = -0.032768 Radius of convergence (given) for eq 1 = 1.88 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.88 Order of pole (three term test) = 2.855e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; Iterations = 40 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 %