##############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=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=100000000; glob_max_minutes=10.0; glob_subiter_method=3; // 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 = 10 estimated_h = -1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -1.3 estimated_steps = 1300000 step_error = 4.385290096535146e-15 est_needed_step_err = 4.385290096535146e-15 opt_iter = 1 Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.040816326530612 glob_desired_digits_correct = 10 estimated_h = -1e-06 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-10 range = -1.3 estimated_steps = 1300000 step_error = 8.949571625581931e-15 est_needed_step_err = 8.949571625581931e-15 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 Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.040816326530612 glob_desired_digits_correct = 10 estimated_h = -2e-06 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-10 range = -1.3 estimated_steps = 650000 step_error = 1.26566055703274e-14 est_needed_step_err = 1.26566055703274e-14 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 Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.040816326530612 glob_desired_digits_correct = 10 estimated_h = -4e-06 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-10 range = -1.3 estimated_steps = 325000 step_error = 1.789914325116386e-14 est_needed_step_err = 1.789914325116386e-14 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 Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.040816326530612 glob_desired_digits_correct = 10 estimated_h = -8e-06 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-10 range = -1.3 estimated_steps = 162500 step_error = 2.531321114065479e-14 est_needed_step_err = 2.531321114065479e-14 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 Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.040816326530612 glob_desired_digits_correct = 10 estimated_h = -1.6e-05 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-10 range = -1.3 estimated_steps = 81250 step_error = 3.579828650232773e-14 est_needed_step_err = 3.579828650232773e-14 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 Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.040816326530612 glob_desired_digits_correct = 10 estimated_h = -3.2e-05 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-10 range = -1.3 estimated_steps = 40625 step_error = 5.062642228130959e-14 est_needed_step_err = 5.062642228130959e-14 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 Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.040816326530612 glob_desired_digits_correct = 10 estimated_h = -6.4e-05 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-10 range = -1.3 estimated_steps = 20312.5 step_error = 7.159657300465545e-14 est_needed_step_err = 7.159657300465545e-14 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 Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.040816326530612 glob_desired_digits_correct = 10 estimated_h = -0.000128 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-10 range = -1.3 estimated_steps = 10156.25 step_error = 1.012528445626192e-13 est_needed_step_err = 1.012528445626192e-13 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 Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.040816326530612 glob_desired_digits_correct = 10 estimated_h = -0.000256 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-10 range = -1.3 estimated_steps = 5078.125 step_error = 1.431931460093109e-13 est_needed_step_err = 1.431931460093109e-13 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 Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.040816326530612 glob_desired_digits_correct = 10 estimated_h = -0.000512 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-10 range = -1.3 estimated_steps = 2539.0625 step_error = 2.025056891252383e-13 est_needed_step_err = 2.025056891252383e-13 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 Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.040816326530612 glob_desired_digits_correct = 10 estimated_h = -0.001024 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-10 range = -1.3 estimated_steps = 1269.53125 step_error = 2.863862920186218e-13 est_needed_step_err = 2.863862920186218e-13 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 Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.040816326530612 glob_desired_digits_correct = 10 estimated_h = -0.002048 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-10 range = -1.3 estimated_steps = 634.765625 step_error = 4.050113782504767e-13 est_needed_step_err = 4.050113782504767e-13 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 Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.040816326530612 glob_desired_digits_correct = 10 estimated_h = -0.004096 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-10 range = -1.3 estimated_steps = 317.3828125 step_error = 5.727725840372436e-13 est_needed_step_err = 5.727725840372436e-13 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 Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.040816326530612 glob_desired_digits_correct = 10 estimated_h = -0.008192 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-10 range = -1.3 estimated_steps = 158.69140625 step_error = 8.100227565009534e-13 est_needed_step_err = 8.100227565009534e-13 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 Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.040816326530612 glob_desired_digits_correct = 10 estimated_h = -0.016384 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-10 range = -1.3 estimated_steps = 79.345703125 step_error = 1.145545168074487e-12 est_needed_step_err = 1.145545168074487e-12 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 Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.040816326530612 glob_desired_digits_correct = 10 estimated_h = -0.032768 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-10 range = -1.3 estimated_steps = 39.6728515625 step_error = 1.620045513001907e-12 est_needed_step_err = 1.620045513001907e-12 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 Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.040816326530612 glob_desired_digits_correct = 10 estimated_h = -0.065536 estimated_answer = 2.040816326530612 desired_abs_gbl_error = 2.040816326530612e-10 range = -1.3 estimated_steps = 19.83642578125 step_error = 2.291090336148974e-12 est_needed_step_err = 2.291090336148974e-12 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 Double H and LOOP opt_iter = 18 SETTING H FOR MAX H SETTING H FOR POLE Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5341 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = -0.7 y[1] (closed_form) = 2.040816326530612 y[1] (numeric) = 2.040816326530612 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 14 Correct digits = 16 h = -0.05340576171874994 Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.86021728515625 y[1] (closed_form) = 1.351399238947492 y[1] (numeric) = 1.351397913831187 absolute error = 1.325116304906615e-06 relative error = 9.805513180092164e-05 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 7 h = -0.05340576171874994 Radius of convergence (given) for eq 1 = 0.8602 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8602 Order of pole (three term test) = 7.702e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.96702880859375 y[1] (closed_form) = 1.069353205118956 y[1] (numeric) = 1.069351655611583 absolute error = 1.549507373077574e-06 relative error = 0.0001449013633344098 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 6 h = -0.05340576171874994 Radius of convergence (given) for eq 1 = 0.967 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.967 Order of pole (three term test) = 2.687e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.12724609375 y[1] (closed_form) = 0.7869778734297919 y[1] (numeric) = 0.7869762091309308 absolute error = 1.664298861059343e-06 relative error = 0.0002114797527668762 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 6 h = -0.05340576171874994 Radius of convergence (given) for eq 1 = 1.127 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.127 Order of pole (three term test) = 4.173e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.2340576171875 y[1] (closed_form) = 0.6566427081817543 y[1] (numeric) = 0.6566410162297507 absolute error = 1.69195200361294e-06 relative error = 0.0002576670665083543 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 6 h = -0.05340576171874994 Radius of convergence (given) for eq 1 = 1.234 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.234 Order of pole (three term test) = 3.943e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.39427490234375 y[1] (closed_form) = 0.5144026297803387 y[1] (numeric) = 0.5144009200241922 absolute error = 1.709756146439645e-06 relative error = 0.0003323770228720931 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = -0.05340576171874994 Radius of convergence (given) for eq 1 = 1.394 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.394 Order of pole (three term test) = 4.798e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.50108642578125 y[1] (closed_form) = 0.443801335348687 y[1] (numeric) = 0.4437996203138217 absolute error = 1.715034865346077e-06 relative error = 0.0003864420245600666 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = -0.05340576171874994 Radius of convergence (given) for eq 1 = 1.501 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.501 Order of pole (three term test) = 2.746e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.6613037109375 y[1] (closed_form) = 0.3623280274364217 y[1] (numeric) = 0.3623263084589128 absolute error = 1.718977508891051e-06 relative error = 0.0004744257630449752 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = -0.05340576171874994 Radius of convergence (given) for eq 1 = 1.661 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.661 Order of pole (three term test) = 7.192e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.768115234375 y[1] (closed_form) = 0.3198739459149033 y[1] (numeric) = 0.3198722255967615 absolute error = 1.720318141773536e-06 relative error = 0.000537811273391799 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = -0.05340576171874994 Radius of convergence (given) for eq 1 = 1.768 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.768 Order of pole (three term test) = 2.915e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.8749267578125 y[1] (closed_form) = 0.2844666679688179 y[1] (numeric) = 0.2844649468281051 absolute error = 1.721140712784841e-06 relative error = 0.0006050412602201625 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = -0.05340576171874994 Radius of convergence (given) for eq 1 = 1.875 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.875 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; Iterations = 25 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 = 10 Minutes 0.0 Seconds Percent Done = 0 %