##############ECHO OF PROBLEM################# ##############temp/sing3postode.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=-2.0; x_end=-0.7; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=100; glob_max_h=0.01; /* # Not Given = 0 */ /* # No Pole = 3 */ /* # Pole = 4 */ glob_type_given_pole=4; /* # Real Part */ array_given_rad_poles[1][1]=0.0; /* # Imag Part */ array_given_rad_poles[1][2]=0.0; /* # Order */ array_given_ord_poles[1][1]=2.0; /* # Not Used */ array_given_ord_poles[1][2]=0.0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.1; glob_look_poles=true; glob_max_iter=10000000; glob_max_minutes=3; 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 desired_abs_gbl_error = 1e-10 range = 1.3 estimated_steps = 1300000 step_error = 7.692307692307693e-17 est_needed_step_err = 7.692307692307693e-17 opt_iter = 1 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 best_h = 2e-06 opt_iter = 2 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 best_h = 4e-06 opt_iter = 3 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 best_h = 8e-06 opt_iter = 4 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 best_h = 1.6e-05 opt_iter = 5 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 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.646976391198811e-78 estimated_step_error = 8.646976391198811e-78 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.666925116673298e-73 estimated_step_error = 5.666925116673298e-73 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.713931972760089e-68 estimated_step_error = 3.713931972760089e-68 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.434035767328666e-63 estimated_step_error = 2.434035767328666e-63 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.595265777626102e-58 estimated_step_error = 1.595265777626102e-58 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.045599359316913e-53 estimated_step_error = 1.045599359316913e-53 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.8540917956248e-49 estimated_step_error = 6.8540917956248e-49 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.494064260848053e-44 estimated_step_error = 4.494064260848053e-44 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.948073954531448e-39 estimated_step_error = 2.948073954531448e-39 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.935788219210894e-34 estimated_step_error = 1.935788219210894e-34 best_h = 0.01 START of Soultion TOP MAIN SOLVE Loop x[1] = -2 y[1] (analytic) = 0.25 y[1] (numeric) = 0.25 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 2.118 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (analytic) = 0.2770083102493075 y[1] (numeric) = 0.2770083102492121 absolute error = 9.54236689665322e-14 relative error = 3.444794449691813e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 1.9 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 2.012 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 1.9 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.8 y[1] (analytic) = 0.308641975308642 y[1] (numeric) = 0.3086419753084012 absolute error = 2.408073740411965e-13 relative error = 7.802158918934764e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 1.8 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.906 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.7 y[1] (analytic) = 0.3460207612456749 y[1] (numeric) = 0.3460207612452071 absolute error = 4.677369602745785e-13 relative error = 1.351759815193531e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.7 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.8 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 1.7 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.6 y[1] (analytic) = 0.3906250000000002 y[1] (numeric) = 0.3906249999991691 absolute error = 8.311129562343922e-13 relative error = 2.127649167960043e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.694 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.5 y[1] (analytic) = 0.4444444444444447 y[1] (numeric) = 0.4444444444430141 absolute error = 1.430577878380745e-12 relative error = 3.218800226356675e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.5 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.588 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 1.5 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.399999999999999 y[1] (analytic) = 0.5102040816326534 y[1] (numeric) = 0.5102040816302 absolute error = 2.453370839816671e-12 relative error = 4.808606846040672e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.4 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.482 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 1.4 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.299999999999999 y[1] (analytic) = 0.5917159763313615 y[1] (numeric) = 0.5917159763270945 absolute error = 4.267031172844327e-12 relative error = 7.211282682106905e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.3 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.376 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 1.3 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.199999999999999 y[1] (analytic) = 0.6944444444444453 y[1] (numeric) = 0.6944444444368166 absolute error = 7.628675469106838e-12 relative error = 1.098529267551383e-09 % Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.2 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.271 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 1.2 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.099999999999999 y[1] (analytic) = 0.8264462809917367 y[1] (numeric) = 0.8264462809775451 absolute error = 1.419153683457353e-11 relative error = 1.717175956983394e-09 % Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.1 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.165 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 1.1 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9999999999999991 y[1] (analytic) = 1.000000000000002 y[1] (numeric) = 0.9999999999721856 absolute error = 2.781619379277345e-11 relative error = 2.78161937927734e-09 % Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.059 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.899999999999999 y[1] (analytic) = 1.23456790123457 y[1] (numeric) = 1.234567901176298 absolute error = 5.827294202731537e-11 relative error = 4.720108304212535e-09 % Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.9 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.9529 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.9 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7999999999999989 y[1] (analytic) = 1.562500000000004 y[1] (numeric) = 1.562499999867173 absolute error = 1.328313015136473e-10 relative error = 8.501203296873404e-09 % Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.8 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.8471 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.8 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; Iterations = 130 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.8 %