##############ECHO OF PROBLEM################# ##############temp/lin_coshpostode.ode################# diff ( y , x , 1 ) = cosh ( 2.0 * x + 3.0 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.1; x_end=2.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=0.000000001; glob_type_given_pole=3; // 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(sinh(2.0*x+3.0)/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-09 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1.9 estimated_steps = 1900000000 step_error = 7.647191129018727e-23 est_needed_step_err = 7.647191129018727e-23 opt_iter = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 6.122941998282746 glob_desired_digits_correct = 16 estimated_h = 1e-09 estimated_answer = 6.122941998282746 desired_abs_gbl_error = 6.122941998282746e-16 range = 1.9 estimated_steps = 1900000000 step_error = 4.682330773276401e-22 est_needed_step_err = 4.682330773276401e-22 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.018875234004473e-252 estimated_step_error = 1.018875234004473e-252 Double H and LOOP opt_iter = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 6.122941998282746 glob_desired_digits_correct = 16 estimated_h = 2e-09 estimated_answer = 6.122941998282746 desired_abs_gbl_error = 6.122941998282746e-16 range = 1.9 estimated_steps = 949999999.9999999 step_error = 6.621815683084387e-22 est_needed_step_err = 6.621815683084387e-22 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.837555950923353e-245 estimated_step_error = 6.837555950923353e-245 Double H and LOOP opt_iter = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 6.122941998282746 glob_desired_digits_correct = 16 estimated_h = 4e-09 estimated_answer = 6.122941998282746 desired_abs_gbl_error = 6.122941998282746e-16 range = 1.9 estimated_steps = 474999999.9999999 step_error = 9.364661546552803e-22 est_needed_step_err = 9.364661546552803e-22 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.588606123688032e-237 estimated_step_error = 4.588606123688032e-237 Double H and LOOP opt_iter = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 6.122941998282746 glob_desired_digits_correct = 16 estimated_h = 8e-09 estimated_answer = 6.122941998282746 desired_abs_gbl_error = 6.122941998282746e-16 range = 1.9 estimated_steps = 237500000 step_error = 1.324363136616877e-21 est_needed_step_err = 1.324363136616877e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.079361442583753e-229 estimated_step_error = 3.079361442583753e-229 Double H and LOOP opt_iter = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 6.122941998282746 glob_desired_digits_correct = 16 estimated_h = 1.6e-08 estimated_answer = 6.122941998282746 desired_abs_gbl_error = 6.122941998282746e-16 range = 1.9 estimated_steps = 118750000 step_error = 1.872932309310561e-21 est_needed_step_err = 1.872932309310561e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.066524481957627e-221 estimated_step_error = 2.066524481957627e-221 Double H and LOOP opt_iter = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 6.122941998282746 glob_desired_digits_correct = 16 estimated_h = 3.2e-08 estimated_answer = 6.122941998282746 desired_abs_gbl_error = 6.122941998282746e-16 range = 1.9 estimated_steps = 59374999.99999999 step_error = 2.648726273233755e-21 est_needed_step_err = 2.648726273233755e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.386821103299093e-213 estimated_step_error = 1.386821103299093e-213 Double H and LOOP opt_iter = 7 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 6.122941998282746 glob_desired_digits_correct = 16 estimated_h = 6.4e-08 estimated_answer = 6.122941998282746 desired_abs_gbl_error = 6.122941998282746e-16 range = 1.9 estimated_steps = 29687500 step_error = 3.745864618621121e-21 est_needed_step_err = 3.745864618621121e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.306798870295882e-206 estimated_step_error = 9.306798870295882e-206 Double H and LOOP opt_iter = 8 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 6.122941998282746 glob_desired_digits_correct = 16 estimated_h = 1.28e-07 estimated_answer = 6.122941998282746 desired_abs_gbl_error = 6.122941998282746e-16 range = 1.9 estimated_steps = 14843750 step_error = 5.29745254646751e-21 est_needed_step_err = 5.29745254646751e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.245686981766529e-198 estimated_step_error = 6.245686981766529e-198 Double H and LOOP opt_iter = 9 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 6.122941998282746 glob_desired_digits_correct = 16 estimated_h = 2.56e-07 estimated_answer = 6.122941998282746 desired_abs_gbl_error = 6.122941998282746e-16 range = 1.9 estimated_steps = 7421874.999999999 step_error = 7.491729237242242e-21 est_needed_step_err = 7.491729237242242e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.191409562522877e-190 estimated_step_error = 4.191409562522877e-190 Double H and LOOP opt_iter = 10 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 6.122941998282746 y[1] (numeric) = 6.122941998282746 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 2.56e-07 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2000000000015745 y[1] (closed_form) = 7.482681694382786 y[1] (numeric) = 7.482681694361508 absolute error = 2.12780904007559e-11 relative error = 2.843645001862001e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 2.56e-07 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.299999999997728 y[1] (closed_form) = 9.142727680266068 y[1] (numeric) = 9.142727680312969 absolute error = 4.690114963068481e-11 relative error = 5.129885879890925e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 2.56e-07 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3999999999884605 y[1] (closed_form) = 11.16970343010312 y[1] (numeric) = 11.16970343033817 absolute error = 2.350510897031199e-10 relative error = 2.104362852371183e-09 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 11 h = 2.56e-07 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.499999999979193 y[1] (closed_form) = 13.64495859799568 y[1] (numeric) = 13.6449585984602 absolute error = 4.645226425736837e-10 relative error = 3.404353624362905e-09 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 11 h = 2.56e-07 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5999999999699256 y[1] (closed_form) = 16.66783386502316 y[1] (numeric) = 16.66783386576798 absolute error = 7.448157646194886e-10 relative error = 4.468581644447855e-09 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 11 h = 2.56e-07 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6999999999606581 y[1] (closed_form) = 20.35964782966381 y[1] (numeric) = 20.35964783075078 absolute error = 1.086970513597407e-09 relative error = 5.33884732531425e-09 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 11 h = 2.56e-07 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7999999999513906 y[1] (closed_form) = 24.86856594912912 y[1] (numeric) = 24.86856595063395 absolute error = 1.504837143784243e-09 relative error = 6.051161723046366e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 2.56e-07 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8999999999421231 y[1] (closed_form) = 30.37554693940491 y[1] (numeric) = 30.375546941419 absolute error = 2.014093780644544e-09 relative error = 6.630642024857651e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 2.56e-07 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9999999999328556 y[1] (closed_form) = 37.1016052839116 y[1] (numeric) = 37.10160528654957 absolute error = 2.637975171637663e-09 relative error = 7.110137557259741e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 2.56e-07 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.099999999966956 y[1] (closed_form) = 45.31668132468752 y[1] (numeric) = 45.31668132452606 absolute error = 1.614566258467676e-10 relative error = 3.56285193723596e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 2.56e-07 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.200000000001057 y[1] (closed_form) = 55.3504749059281 y[1] (numeric) = 55.35047490234528 absolute error = 3.582812269087299e-09 relative error = 6.472956691295842e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 2.56e-07 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.300000000035157 y[1] (closed_form) = 67.60567739536285 y[1] (numeric) = 67.60567738760189 absolute error = 7.760959874758555e-09 relative error = 1.147974574586673e-08 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 10 h = 2.56e-07 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.400000000069258 y[1] (closed_form) = 82.57413310016385 y[1] (numeric) = 82.57413308729856 absolute error = 1.286528572563839e-08 relative error = 1.558028554781504e-08 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 10 h = 2.56e-07 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.500000000103358 y[1] (closed_form) = 100.8565787059886 y[1] (numeric) = 100.85657868689 absolute error = 1.909859292936744e-08 relative error = 1.893638786324746e-08 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 10 h = 2.56e-07 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.600000000137459 y[1] (closed_form) = 123.1867529495215 y[1] (numeric) = 123.1867529228087 absolute error = 2.671279730748211e-08 relative error = 2.168479699958344e-08 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 10 h = 2.56e-07 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.70000000017156 y[1] (closed_form) = 150.4608441303286 y[1] (numeric) = 150.4608440943198 absolute error = 3.600871423259377e-08 relative error = 2.393228247570057e-08 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 10 h = 2.56e-07 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.80000000020566 y[1] (closed_form) = 183.7734572940739 y[1] (numeric) = 183.7734572466986 absolute error = 4.737523795483867e-08 relative error = 2.577915149032045e-08 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 10 h = 2.56e-07 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.900000000239761 y[1] (closed_form) = 224.4615445764518 y[1] (numeric) = 224.4615445152096 absolute error = 6.124218998593278e-08 relative error = 2.728404551500965e-08 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 10 h = 2.56e-07 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = cosh ( 2.0 * x + 3.0 ) ; Iterations = 7421875 Total Elapsed Time = 32.0 Seconds Elapsed Time(since restart) = 32.0 Seconds Time to Timeout = 2 Minutes 28.0 Seconds Percent Done = 100 %