##############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; 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]=6.0; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=3.0; 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 - 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 = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 1000000 step_error = 5e-21 est_needed_step_err = 5e-21 opt_iter = 1 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 1000000 step_error = 5e-21 est_needed_step_err = 5e-21 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 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 500000 step_error = 7.071067811865475e-21 est_needed_step_err = 7.071067811865475e-21 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 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 250000 step_error = 9.999999999999999e-21 est_needed_step_err = 9.999999999999999e-21 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 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 125000 step_error = 1.414213562373095e-20 est_needed_step_err = 1.414213562373095e-20 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 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 62500 step_error = 2e-20 est_needed_step_err = 2e-20 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 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 31250 step_error = 2.82842712474619e-20 est_needed_step_err = 2.82842712474619e-20 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 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 15625 step_error = 4e-20 est_needed_step_err = 4e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.161744097799704e-78 estimated_step_error = 2.161744097799704e-78 Double H and LOOP opt_iter = 8 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 7812.5 step_error = 5.65685424949238e-20 est_needed_step_err = 5.65685424949238e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.41673127916833e-73 estimated_step_error = 1.41673127916833e-73 Double H and LOOP opt_iter = 9 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 3906.25 step_error = 8e-20 est_needed_step_err = 8e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.284829931900477e-69 estimated_step_error = 9.284829931900477e-69 Double H and LOOP opt_iter = 10 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 1953.125 step_error = 1.131370849898476e-19 est_needed_step_err = 1.131370849898476e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.085089418323007e-64 estimated_step_error = 6.085089418323007e-64 Double H and LOOP opt_iter = 11 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 976.5625 step_error = 1.6e-19 est_needed_step_err = 1.6e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.988164444072296e-59 estimated_step_error = 3.988164444072296e-59 Double H and LOOP opt_iter = 12 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 488.28125 step_error = 2.262741699796952e-19 est_needed_step_err = 2.262741699796952e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.613998398329204e-54 estimated_step_error = 2.613998398329204e-54 Double H and LOOP opt_iter = 13 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 244.140625 step_error = 3.2e-19 est_needed_step_err = 3.2e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.713522949099779e-49 estimated_step_error = 1.713522949099779e-49 Double H and LOOP opt_iter = 14 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 122.0703125 step_error = 4.525483399593904e-19 est_needed_step_err = 4.525483399593904e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.123516066226922e-44 estimated_step_error = 1.123516066226922e-44 Double H and LOOP opt_iter = 15 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 61.03515625 step_error = 6.4e-19 est_needed_step_err = 6.4e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.37018493953904e-40 estimated_step_error = 7.37018493953904e-40 Double H and LOOP opt_iter = 16 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 30.517578125 step_error = 9.050966799187808e-19 est_needed_step_err = 9.050966799187808e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.839470827003089e-35 estimated_step_error = 4.839470827003089e-35 Double H and LOOP opt_iter = 17 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.065536 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 15.2587890625 step_error = 1.28e-18 est_needed_step_err = 1.28e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.183917781133918e-30 estimated_step_error = 3.183917781133918e-30 Double H and LOOP opt_iter = 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.052 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) = 0.0625 y[1] (numeric) = 0.0625 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 = 4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 7.641e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (closed_form) = 0.06574621959237345 y[1] (numeric) = 0.06574621956038727 absolute error = 3.198617759547773e-11 relative error = 4.865097612272162e-08 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 10 h = 0.1 Radius of convergence (given) for eq 1 = 3.9 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.9 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (closed_form) = 0.06925207756232687 y[1] (numeric) = 0.06925207749112541 absolute error = 7.12014613934997e-11 relative error = 1.028149102522136e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 Radius of convergence (given) for eq 1 = 3.8 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.8 Order of pole (three term test) = 8.747e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (closed_form) = 0.07304601899196494 y[1] (numeric) = 0.07304601887242848 absolute error = 1.195364640604879e-10 relative error = 1.636454192988079e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 Radius of convergence (given) for eq 1 = 3.7 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.7 Order of pole (three term test) = 3.93e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (closed_form) = 0.0771604938271605 y[1] (numeric) = 0.07716049364771317 absolute error = 1.794473319938206e-10 relative error = 2.325637422639914e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 Radius of convergence (given) for eq 1 = 3.6 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.6 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (closed_form) = 0.08163265306122451 y[1] (numeric) = 0.08163265280707702 absolute error = 2.541474947159728e-10 relative error = 3.113306810270665e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.5 Order of pole (three term test) = 8.903e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.600000000000001 y[1] (closed_form) = 0.08650519031141872 y[1] (numeric) = 0.08650518996354627 absolute error = 3.478724530658894e-10 relative error = 4.02140555744168e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.700000000000001 y[1] (closed_form) = 0.09182736455463732 y[1] (numeric) = 0.09182736408838833 absolute error = 4.662489838658246e-10 relative error = 5.077451434298828e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 Radius of convergence (given) for eq 1 = 3.3 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.3 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.800000000000001 y[1] (closed_form) = 0.09765625000000004 y[1] (numeric) = 0.09765624938318546 absolute error = 6.168145855189877e-10 relative error = 6.316181355714431e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 Radius of convergence (given) for eq 1 = 3.2 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.2 Order of pole (three term test) = 3.229e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.900000000000001 y[1] (closed_form) = 0.1040582726326744 y[1] (numeric) = 0.1040582718229187 absolute error = 8.097556791764049e-10 relative error = 7.781752076885247e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 Radius of convergence (given) for eq 1 = 3.1 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.1 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 - 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 %