##############ECHO OF PROBLEM################# ##############temp/sing3postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; ! // BEGIN FIRST INPUT BLOCK Digits=16; max_terms=20; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=-2.0; 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]=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 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 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 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.152559056001943e-102 estimated_step_error = 7.152559056001943e-102 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1.3 estimated_steps = 650000 step_error = 6.201736729460424e-21 est_needed_step_err = 6.201736729460424e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.68750220588339e-97 estimated_step_error = 4.68750220588339e-97 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1.3 estimated_steps = 325000 step_error = 8.770580193070291e-21 est_needed_step_err = 8.770580193070291e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.072002891296846e-92 estimated_step_error = 3.072002891296846e-92 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1.3 estimated_steps = 162500 step_error = 1.240347345892085e-20 est_needed_step_err = 1.240347345892085e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.013269709684182e-87 estimated_step_error = 2.013269709684182e-87 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1.3 estimated_steps = 81250 step_error = 1.754116038614058e-20 est_needed_step_err = 1.754116038614058e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.319418920555435e-82 estimated_step_error = 1.319418920555435e-82 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1.3 estimated_steps = 40625 step_error = 2.480694691784169e-20 est_needed_step_err = 2.480694691784169e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.646976391198815e-78 estimated_step_error = 8.646976391198815e-78 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1.3 estimated_steps = 20312.5 step_error = 3.508232077228117e-20 est_needed_step_err = 3.508232077228117e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.666925116673318e-73 estimated_step_error = 5.666925116673318e-73 Double H and LOOP opt_iter = 8 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1.3 estimated_steps = 10156.25 step_error = 4.961389383568339e-20 est_needed_step_err = 4.961389383568339e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.713931972760191e-68 estimated_step_error = 3.713931972760191e-68 Double H and LOOP opt_iter = 9 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1.3 estimated_steps = 5078.125 step_error = 7.016464154456233e-20 est_needed_step_err = 7.016464154456233e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.434035767329203e-63 estimated_step_error = 2.434035767329203e-63 Double H and LOOP opt_iter = 10 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1.3 estimated_steps = 2539.0625 step_error = 9.922778767136678e-20 est_needed_step_err = 9.922778767136678e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.595265777628918e-58 estimated_step_error = 1.595265777628918e-58 Double H and LOOP opt_iter = 11 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1.3 estimated_steps = 1269.53125 step_error = 1.403292830891247e-19 est_needed_step_err = 1.403292830891247e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.045599359331682e-53 estimated_step_error = 1.045599359331682e-53 Double H and LOOP opt_iter = 12 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1.3 estimated_steps = 634.765625 step_error = 1.984555753427336e-19 est_needed_step_err = 1.984555753427336e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.854091796399115e-49 estimated_step_error = 6.854091796399115e-49 Double H and LOOP opt_iter = 13 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1.3 estimated_steps = 317.3828125 step_error = 2.806585661782493e-19 est_needed_step_err = 2.806585661782493e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.494064264907686e-44 estimated_step_error = 4.494064264907686e-44 Double H and LOOP opt_iter = 14 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1.3 estimated_steps = 158.69140625 step_error = 3.969111506854671e-19 est_needed_step_err = 3.969111506854671e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.948073975815616e-39 estimated_step_error = 2.948073975815616e-39 Double H and LOOP opt_iter = 15 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1.3 estimated_steps = 79.345703125 step_error = 5.613171323564987e-19 est_needed_step_err = 5.613171323564987e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.935788330801236e-34 estimated_step_error = 1.935788330801236e-34 Double H and LOOP opt_iter = 16 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1.3 estimated_steps = 39.6728515625 step_error = 7.938223013709342e-19 est_needed_step_err = 7.938223013709342e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.273567112453567e-29 estimated_step_error = 1.273567112453567e-29 Double H and LOOP opt_iter = 17 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.065536 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1.3 estimated_steps = 19.83642578125 step_error = 1.122634264712997e-18 est_needed_step_err = 1.122634264712997e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.411814337987063e-25 estimated_step_error = 8.411814337987063e-25 Double H and LOOP opt_iter = 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.526 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] = -2 y[1] (closed_form) = 0.25 y[1] (numeric) = 0.25 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 7.641e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (closed_form) = 0.2770083102493075 y[1] (numeric) = 0.277008301656629 absolute error = 8.592678513164032e-09 relative error = 3.101956943252215e-06 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 8 h = 0.1 Radius of convergence (given) for eq 1 = 1.9 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.9 Order of pole (three term test) = 8.747e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.8 y[1] (closed_form) = 0.308641975308642 y[1] (numeric) = 0.3086419536970876 absolute error = 2.16115543794082e-08 relative error = 7.002143618928257e-06 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 8 h = 0.1 Radius of convergence (given) for eq 1 = 1.8 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.7 y[1] (closed_form) = 0.3460207612456749 y[1] (numeric) = 0.3460207194545793 absolute error = 4.179109558410943e-08 relative error = 1.207762662380762e-05 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 7 h = 0.1 Radius of convergence (given) for eq 1 = 1.7 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.6 y[1] (closed_form) = 0.3906250000000002 y[1] (numeric) = 0.3906249261247441 absolute error = 7.387525602364775e-08 relative error = 1.891206554205382e-05 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 7 h = 0.1 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 3.229e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.5 y[1] (closed_form) = 0.4444444444444447 y[1] (numeric) = 0.4444443180796188 absolute error = 1.263648259364203e-07 relative error = 2.843208583569455e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 Radius of convergence (given) for eq 1 = 1.5 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.5 Order of pole (three term test) = 3.726e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.399999999999999 y[1] (closed_form) = 0.5102040816326534 y[1] (numeric) = 0.5102038665750483 absolute error = 2.150576050574671e-07 relative error = 4.215129059126352e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 Radius of convergence (given) for eq 1 = 1.4 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.4 Order of pole (three term test) = 7.524e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.299999999999999 y[1] (closed_form) = 0.5917159763313615 y[1] (numeric) = 0.5917156057807762 absolute error = 3.705505853268676e-07 relative error = 6.262304892024055e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 Radius of convergence (given) for eq 1 = 1.3 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.3 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.199999999999999 y[1] (closed_form) = 0.6944444444444453 y[1] (numeric) = 0.6944437894714137 absolute error = 6.549730315885682e-07 relative error = 9.43161165487537e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 Radius of convergence (given) for eq 1 = 1.2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.2 Order of pole (three term test) = 2.362e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.099999999999999 y[1] (closed_form) = 0.8264462809917367 y[1] (numeric) = 0.8264450794216911 absolute error = 1.201570045572531e-06 relative error = 0.000145389975514276 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 6 h = 0.1 Radius of convergence (given) for eq 1 = 1.1 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.1 Order of pole (three term test) = 2.778e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9999999999999992 y[1] (closed_form) = 1.000000000000002 y[1] (numeric) = 0.9999976850307339 absolute error = 2.31496926783592e-06 relative error = 0.0002314969267835916 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 6 h = 0.1 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 2.547e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8999999999999992 y[1] (closed_form) = 1.23456790123457 y[1] (numeric) = 1.234563154765524 absolute error = 4.746469046468249e-06 relative error = 0.0003844639927639275 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 6 h = 0.1 SETTING H FOR POLE Radius of convergence (given) for eq 1 = 0.9 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9 Order of pole (three term test) = 3.455e-14 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = -0.7289999999999989 y[1] (closed_form) = 1.881676423158926 y[1] (numeric) = 1.881664968848698 absolute error = 1.145431022875343e-05 relative error = 0.0006087290082278932 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 6 h = 0.08100000000000018 SETTING H FOR POLE Radius of convergence (given) for eq 1 = 0.729 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.729 Order of pole (three term test) = 2.974e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; Iterations = 14 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 109 %