##############ECHO OF PROBLEM################# ##############temp/cosh_sqrtpostode.ode################# diff ( y , x , 1 ) = cosh ( sqrt ( 0.1 * x + 0.2 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-1.9; x_end=-1.8; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.01; glob_upper_ratio_limit=1.001; glob_lower_ratio_limit=0.999; glob_type_given_pole=1; array_given_rad_poles[1][1]=-2.0; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=0.5; 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(20.0 * sqrt(0.1 * x + 0.2) * sinh( sqrt(0.1 * x + 0.2)) - 20.0 * cosh( sqrt(0.1 * x + 0.2))); } /* 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 = 0.09999999999999987 estimated_steps = 99999.99999999987 step_error = 1.05409255338946e-20 est_needed_step_err = 1.05409255338946e-20 opt_iter = 1 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09968 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 min_size = 19.89974986107638 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 19.89974986107638 desired_abs_gbl_error = 1.989974986107638e-15 range = 0.09999999999999987 estimated_steps = 99999.99999999987 step_error = 2.097617814287356e-19 est_needed_step_err = 2.097617814287356e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.689350542413945e-138 estimated_step_error = 4.689350542413945e-138 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09968 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 min_size = 19.89974986107638 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 19.89974986107638 desired_abs_gbl_error = 1.989974986107638e-15 range = 0.09999999999999987 estimated_steps = 49999.99999999993 step_error = 2.966479561640587e-19 est_needed_step_err = 2.966479561640587e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.146955635139175e-130 estimated_step_error = 3.146955635139175e-130 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09968 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 min_size = 19.89974986107638 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 19.89974986107638 desired_abs_gbl_error = 1.989974986107638e-15 range = 0.09999999999999987 estimated_steps = 24999.99999999997 step_error = 4.195235628574713e-19 est_needed_step_err = 4.195235628574713e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.111867061153189e-122 estimated_step_error = 2.111867061153189e-122 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09968 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 min_size = 19.89974986107638 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 19.89974986107638 desired_abs_gbl_error = 1.989974986107638e-15 range = 0.09999999999999987 estimated_steps = 12499.99999999998 step_error = 5.932959123281175e-19 est_needed_step_err = 5.932959123281175e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.417224337336802e-114 estimated_step_error = 1.417224337336802e-114 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09968 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 min_size = 19.89974986107638 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 19.89974986107638 desired_abs_gbl_error = 1.989974986107638e-15 range = 0.09999999999999987 estimated_steps = 6249.999999999992 step_error = 8.390471257149426e-19 est_needed_step_err = 8.390471257149426e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.510487192989343e-107 estimated_step_error = 9.510487192989343e-107 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09968 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 min_size = 19.89974986107638 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 19.89974986107638 desired_abs_gbl_error = 1.989974986107638e-15 range = 0.09999999999999987 estimated_steps = 3124.999999999996 step_error = 1.186591824656235e-18 est_needed_step_err = 1.186591824656235e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.38191780356733e-99 estimated_step_error = 6.38191780356733e-99 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09968 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 min_size = 19.89974986107638 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 19.89974986107638 desired_abs_gbl_error = 1.989974986107638e-15 range = 0.09999999999999987 estimated_steps = 1562.499999999998 step_error = 1.678094251429885e-18 est_needed_step_err = 1.678094251429885e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.282212437691655e-91 estimated_step_error = 4.282212437691655e-91 Double H and LOOP opt_iter = 8 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09968 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 min_size = 19.89974986107638 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 19.89974986107638 desired_abs_gbl_error = 1.989974986107638e-15 range = 0.09999999999999987 estimated_steps = 781.249999999999 step_error = 2.37318364931247e-18 est_needed_step_err = 2.37318364931247e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.8729121973868e-83 estimated_step_error = 2.8729121973868e-83 Double H and LOOP opt_iter = 9 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09968 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 min_size = 19.89974986107638 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 19.89974986107638 desired_abs_gbl_error = 1.989974986107638e-15 range = 0.09999999999999987 estimated_steps = 390.6249999999995 step_error = 3.35618850285977e-18 est_needed_step_err = 3.35618850285977e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.926863123278842e-75 estimated_step_error = 1.926863123278842e-75 Double H and LOOP opt_iter = 10 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09968 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 min_size = 19.89974986107638 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 19.89974986107638 desired_abs_gbl_error = 1.989974986107638e-15 range = 0.09999999999999987 estimated_steps = 195.3124999999997 step_error = 4.74636729862494e-18 est_needed_step_err = 4.74636729862494e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.291601204459813e-67 estimated_step_error = 1.291601204459813e-67 Double H and LOOP opt_iter = 11 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09968 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 min_size = 19.89974986107638 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 19.89974986107638 desired_abs_gbl_error = 1.989974986107638e-15 range = 0.09999999999999987 estimated_steps = 97.65624999999987 step_error = 6.712377005719541e-18 est_needed_step_err = 6.712377005719541e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.647796455898528e-60 estimated_step_error = 8.647796455898528e-60 Double H and LOOP opt_iter = 12 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09968 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 min_size = 19.89974986107638 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 19.89974986107638 desired_abs_gbl_error = 1.989974986107638e-15 range = 0.09999999999999987 estimated_steps = 48.82812499999994 step_error = 9.49273459724988e-18 est_needed_step_err = 9.49273459724988e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.776789965708514e-52 estimated_step_error = 5.776789965708514e-52 Double H and LOOP opt_iter = 13 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09968 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 min_size = 19.89974986107638 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 19.89974986107638 desired_abs_gbl_error = 1.989974986107638e-15 range = 0.09999999999999987 estimated_steps = 24.41406249999997 step_error = 1.342475401143908e-17 est_needed_step_err = 1.342475401143908e-17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.841461419634064e-44 estimated_step_error = 3.841461419634064e-44 Double H and LOOP opt_iter = 14 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09968 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 min_size = 19.89974986107638 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 19.89974986107638 desired_abs_gbl_error = 1.989974986107638e-15 range = 0.09999999999999987 estimated_steps = 12.20703124999998 step_error = 1.898546919449976e-17 est_needed_step_err = 1.898546919449976e-17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.53188347629922e-36 estimated_step_error = 2.53188347629922e-36 Double H and LOOP opt_iter = 15 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL SETTING H FOR POLE Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06084 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (closed_form) = -19.89974986107638 y[1] (numeric) = -19.89974986107638 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.006083779613909593 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09968 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.887832440772181 y[1] (closed_form) = -19.88751770567766 y[1] (numeric) = -19.88751957740098 absolute error = 1.871723327440122e-06 relative error = 9.411548264295282e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.006083779613909593 Radius of convergence (given) for eq 1 = 0.1122 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1118 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.875664881544362 y[1] (closed_form) = -19.87527813395764 y[1] (numeric) = -19.87528187593071 absolute error = 3.741973067405979e-06 relative error = 1.882727397415728e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.006083779613909593 Radius of convergence (given) for eq 1 = 0.1243 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1239 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.869581101930452 y[1] (closed_form) = -19.86915556650749 y[1] (numeric) = -19.86916024316542 absolute error = 4.676657930247075e-06 relative error = 2.353727572665594e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.006083779613909593 Radius of convergence (given) for eq 1 = 0.1304 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.13 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.857413542702633 y[1] (closed_form) = -19.85690486748748 y[1] (numeric) = -19.85691141280758 absolute error = 6.545320097472995e-06 relative error = 3.296243871415185e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.006083779613909593 Radius of convergence (given) for eq 1 = 0.1426 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1421 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.845245983474814 y[1] (closed_form) = -19.84464674838848 y[1] (numeric) = -19.8446551616078 absolute error = 8.413219319436394e-06 relative error = 4.239540983575131e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.006083779613909593 Radius of convergence (given) for eq 1 = 0.1548 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1543 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.839162203860905 y[1] (closed_form) = -19.83851490583957 y[1] (numeric) = -19.83852425277814 absolute error = 9.346938568910446e-06 relative error = 4.711511226154901e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.006083779613909593 Radius of convergence (given) for eq 1 = 0.1608 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1603 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.826994644633086 y[1] (closed_form) = -19.82624565380316 y[1] (numeric) = -19.82625686780969 absolute error = 1.121400653403271e-05 relative error = 5.656142231790407e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.006083779613909593 Radius of convergence (given) for eq 1 = 0.173 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1724 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.814827085405267 y[1] (closed_form) = -19.81396897792893 y[1] (numeric) = -19.81398205860811 absolute error = 1.308067918515121e-05 relative error = 6.601746071027957e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.006083779613909593 Radius of convergence (given) for eq 1 = 0.1852 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1846 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.808743305791358 y[1] (closed_form) = -19.80782785558268 y[1] (numeric) = -19.80784186948152 absolute error = 1.401389884136961e-05 relative error = 7.074929640717724e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.006083779613909593 Radius of convergence (given) for eq 1 = 0.1913 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1906 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = cosh ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 17 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 109.5 %