##############ECHO OF PROBLEM################# ##############temp/sing6postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=30; max_terms=20; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=2.0; x_end=3.0; glob_max_h=0.5; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=100; /* # Not Given = 0 */ /* # No Pole = 3 */ /* # Pole = 4 */ glob_type_given_pole=4; /* # Real Part */ array_given_rad_poles[1][1]=6.0; /* # Imag Part */ array_given_rad_poles[1][2]=0.0; /* # Order */ array_given_ord_poles[1][1]=3.0; /* # 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 - 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 = 10 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 1000000 step_error = 1e-16 est_needed_step_err = 1e-16 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.728484426316951e-107 estimated_step_error = 2.728484426316951e-107 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 = 1.788139764000486e-102 estimated_step_error = 1.788139764000486e-102 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 = 1.171875551470848e-97 estimated_step_error = 1.171875551470848e-97 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 = 7.680007228242115e-93 estimated_step_error = 7.680007228242115e-93 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 = 5.033174274210456e-88 estimated_step_error = 5.033174274210456e-88 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 = 3.298547301388589e-83 estimated_step_error = 3.298547301388589e-83 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 = 2.161744097799703e-78 estimated_step_error = 2.161744097799703e-78 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 = 1.416731279168325e-73 estimated_step_error = 1.416731279168325e-73 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 = 9.284829931900222e-69 estimated_step_error = 9.284829931900222e-69 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 = 6.085089418321664e-64 estimated_step_error = 6.085089418321664e-64 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 = 3.988164444065254e-59 estimated_step_error = 3.988164444065254e-59 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 = 2.613998398292282e-54 estimated_step_error = 2.613998398292282e-54 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 = 1.7135229489062e-49 estimated_step_error = 1.7135229489062e-49 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 = 1.123516065212013e-44 estimated_step_error = 1.123516065212013e-44 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 = 7.37018488632862e-40 estimated_step_error = 7.37018488632862e-40 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.839470548027236e-35 estimated_step_error = 4.839470548027236e-35 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.183916318497001e-30 estimated_step_error = 3.183916318497001e-30 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.102945916066928e-25 estimated_step_error = 2.102945916066928e-25 best_h = 0.262144 opt_iter = 19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.400082281654855e-20 estimated_step_error = 1.400082281654855e-20 best_h = 0.524288 opt_iter = 20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.475301328483421e-16 estimated_step_error = 9.475301328483421e-16 best_h = 0.5 START of Soultion TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 0.0625 y[1] (numeric) = 0.0625 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 Radius of convergence (ratio test) for eq 1 = 4.235 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (analytic) = 0.06574621959237345 y[1] (numeric) = 0.06574621956038727 absolute error = 3.198617759547773e-11 relative error = 4.865097612272162e-08 % Correct digits = 10 h = 0.1 Radius of convergence (given) for eq 1 = 3.9 Order of pole (given) = 3 Radius of convergence (ratio test) for eq 1 = 4.129 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 3.9 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (analytic) = 0.06925207756232687 y[1] (numeric) = 0.06925207749112541 absolute error = 7.12014613934997e-11 relative error = 1.028149102522136e-07 % Correct digits = 9 h = 0.1 Radius of convergence (given) for eq 1 = 3.8 Order of pole (given) = 3 Radius of convergence (ratio test) for eq 1 = 4.024 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 3.8 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (analytic) = 0.07304601899196494 y[1] (numeric) = 0.07304601887242848 absolute error = 1.195364640604879e-10 relative error = 1.636454192988079e-07 % Correct digits = 9 h = 0.1 Radius of convergence (given) for eq 1 = 3.7 Order of pole (given) = 3 Radius of convergence (ratio test) for eq 1 = 3.918 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 3.7 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (analytic) = 0.0771604938271605 y[1] (numeric) = 0.07716049364771317 absolute error = 1.794473319938206e-10 relative error = 2.325637422639914e-07 % Correct digits = 9 h = 0.1 Radius of convergence (given) for eq 1 = 3.6 Order of pole (given) = 3 Radius of convergence (ratio test) for eq 1 = 3.812 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 3.6 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (analytic) = 0.08163265306122451 y[1] (numeric) = 0.08163265280707702 absolute error = 2.541474947159728e-10 relative error = 3.113306810270665e-07 % Correct digits = 9 h = 0.1 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 3 Radius of convergence (ratio test) for eq 1 = 3.706 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 3.5 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.600000000000001 y[1] (analytic) = 0.08650519031141872 y[1] (numeric) = 0.08650518996354627 absolute error = 3.478724530658894e-10 relative error = 4.02140555744168e-07 % Correct digits = 9 h = 0.1 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 3 Radius of convergence (ratio test) for eq 1 = 3.6 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 3.4 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.700000000000001 y[1] (analytic) = 0.09182736455463732 y[1] (numeric) = 0.09182736408838833 absolute error = 4.662489838658246e-10 relative error = 5.077451434298828e-07 % Correct digits = 9 h = 0.1 Radius of convergence (given) for eq 1 = 3.3 Order of pole (given) = 3 Radius of convergence (ratio test) for eq 1 = 3.494 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 3.3 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.800000000000001 y[1] (analytic) = 0.09765625000000004 y[1] (numeric) = 0.09765624938318546 absolute error = 6.168145855189877e-10 relative error = 6.316181355714431e-07 % Correct digits = 9 h = 0.1 Radius of convergence (given) for eq 1 = 3.2 Order of pole (given) = 3 Radius of convergence (ratio test) for eq 1 = 3.388 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 3.2 Order of pole (three term test) = 18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.900000000000001 y[1] (analytic) = 0.1040582726326744 y[1] (numeric) = 0.1040582718229187 absolute error = 8.097556791764049e-10 relative error = 7.781752076885247e-07 % Correct digits = 9 h = 0.1 Radius of convergence (given) for eq 1 = 3.1 Order of pole (given) = 3 Radius of convergence (ratio test) for eq 1 = 3.282 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 3.1 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 - 6.0 ) / ( x - 6.0 ) / ( x - 6.0) ; Iterations = 10 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 110 %