##############ECHO OF PROBLEM################# ##############temp/lin_tanhpostode.ode################# diff ( y , x , 1 ) = tanh ( 3.0 * x + 1.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=1.1; x_end=2.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; 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(ln(cosh(3.0*x + 1.0))/3.0); } /* 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 = 0.8999999999999999 estimated_steps = 900000 step_error = 2.635231383473649e-21 est_needed_step_err = 2.635231383473649e-21 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 = 1.20234563609611 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1.20234563609611 desired_abs_gbl_error = 1.20234563609611e-16 range = 0.8999999999999999 estimated_steps = 900000 step_error = 3.168458954023058e-21 est_needed_step_err = 3.168458954023058e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.565718975416627e-225 estimated_step_error = 4.565718975416627e-225 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 = 1.20234563609611 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1.20234563609611 desired_abs_gbl_error = 1.20234563609611e-16 range = 0.8999999999999999 estimated_steps = 450000 step_error = 4.480877624601879e-21 est_needed_step_err = 4.480877624601879e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.137537264133354e-214 estimated_step_error = 3.137537264133354e-214 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 = 1.20234563609611 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1.20234563609611 desired_abs_gbl_error = 1.20234563609611e-16 range = 0.8999999999999999 estimated_steps = 225000 step_error = 6.336917908046116e-21 est_needed_step_err = 6.336917908046116e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.15609791898744e-203 estimated_step_error = 2.15609791898744e-203 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 = 1.20234563609611 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1.20234563609611 desired_abs_gbl_error = 1.20234563609611e-16 range = 0.8999999999999999 estimated_steps = 112500 step_error = 8.961755249203758e-21 est_needed_step_err = 8.961755249203758e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.481657460554953e-192 estimated_step_error = 1.481657460554953e-192 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 = 1.20234563609611 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1.20234563609611 desired_abs_gbl_error = 1.20234563609611e-16 range = 0.8999999999999999 estimated_steps = 56250 step_error = 1.267383581609223e-20 est_needed_step_err = 1.267383581609223e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.018184852464881e-181 estimated_step_error = 1.018184852464881e-181 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 = 1.20234563609611 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1.20234563609611 desired_abs_gbl_error = 1.20234563609611e-16 range = 0.8999999999999999 estimated_steps = 28125 step_error = 1.792351049840752e-20 est_needed_step_err = 1.792351049840752e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.996880023136947e-171 estimated_step_error = 6.996880023136947e-171 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 = 1.20234563609611 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1.20234563609611 desired_abs_gbl_error = 1.20234563609611e-16 range = 0.8999999999999999 estimated_steps = 14062.5 step_error = 2.534767163218446e-20 est_needed_step_err = 2.534767163218446e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.808173978498614e-160 estimated_step_error = 4.808173978498614e-160 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 = 1.20234563609611 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1.20234563609611 desired_abs_gbl_error = 1.20234563609611e-16 range = 0.8999999999999999 estimated_steps = 7031.25 step_error = 3.584702099681503e-20 est_needed_step_err = 3.584702099681503e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.304089656080091e-149 estimated_step_error = 3.304089656080091e-149 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 = 1.20234563609611 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 1.20234563609611 desired_abs_gbl_error = 1.20234563609611e-16 range = 0.8999999999999999 estimated_steps = 3515.625 step_error = 5.069534326436892e-20 est_needed_step_err = 5.069534326436892e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.270467443850138e-138 estimated_step_error = 2.270467443850138e-138 Double H and LOOP opt_iter = 10 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 = 1.20234563609611 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 1.20234563609611 desired_abs_gbl_error = 1.20234563609611e-16 range = 0.8999999999999999 estimated_steps = 1757.8125 step_error = 7.169404199363006e-20 est_needed_step_err = 7.169404199363006e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.560135602471466e-127 estimated_step_error = 1.560135602471466e-127 Double H and LOOP opt_iter = 11 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 = 1.20234563609611 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 1.20234563609611 desired_abs_gbl_error = 1.20234563609611e-16 range = 0.8999999999999999 estimated_steps = 878.90625 step_error = 1.013906865287378e-19 est_needed_step_err = 1.013906865287378e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.071955227319964e-116 estimated_step_error = 1.071955227319964e-116 Double H and LOOP opt_iter = 12 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 = 1.20234563609611 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 1.20234563609611 desired_abs_gbl_error = 1.20234563609611e-16 range = 0.8999999999999999 estimated_steps = 439.453125 step_error = 1.433880839872601e-19 est_needed_step_err = 1.433880839872601e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.364197404526034e-106 estimated_step_error = 7.364197404526034e-106 Double H and LOOP opt_iter = 13 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 = 1.20234563609611 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 1.20234563609611 desired_abs_gbl_error = 1.20234563609611e-16 range = 0.8999999999999999 estimated_steps = 219.7265625 step_error = 2.027813730574757e-19 est_needed_step_err = 2.027813730574757e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.057585278815116e-95 estimated_step_error = 5.057585278815116e-95 Double H and LOOP opt_iter = 14 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 = 1.20234563609611 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 1.20234563609611 desired_abs_gbl_error = 1.20234563609611e-16 range = 0.8999999999999999 estimated_steps = 109.86328125 step_error = 2.867761679745202e-19 est_needed_step_err = 2.867761679745202e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.471357165770607e-84 estimated_step_error = 3.471357165770607e-84 Double H and LOOP opt_iter = 15 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 = 1.20234563609611 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 1.20234563609611 desired_abs_gbl_error = 1.20234563609611e-16 range = 0.8999999999999999 estimated_steps = 54.931640625 step_error = 4.055627461149514e-19 est_needed_step_err = 4.055627461149514e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.379759145788281e-73 estimated_step_error = 2.379759145788281e-73 Double H and LOOP opt_iter = 16 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 = 1.20234563609611 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 1.20234563609611 desired_abs_gbl_error = 1.20234563609611e-16 range = 0.8999999999999999 estimated_steps = 27.4658203125 step_error = 5.735523359490405e-19 est_needed_step_err = 5.735523359490405e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.627519000328652e-62 estimated_step_error = 1.627519000328652e-62 Double H and LOOP opt_iter = 17 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 = 1.20234563609611 glob_desired_digits_correct = 16 estimated_h = 0.065536 estimated_answer = 1.20234563609611 desired_abs_gbl_error = 1.20234563609611e-16 range = 0.8999999999999999 estimated_steps = 13.73291015625 step_error = 8.111254922299028e-19 est_needed_step_err = 8.111254922299028e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.107781922059004e-51 estimated_step_error = 1.107781922059004e-51 Double H and LOOP opt_iter = 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL 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 START of Soultion TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (closed_form) = 1.20234563609611 y[1] (numeric) = 1.20234563609611 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.09 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] = 1.19 y[1] (closed_form) = 1.292320033671564 y[1] (numeric) = 1.292320033671565 absolute error = 4.440892098500626e-16 relative error = 3.436371783143968e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.09 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] = 1.28 y[1] (closed_form) = 1.382305112996481 y[1] (numeric) = 1.382305112996481 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.09 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] = 1.37 y[1] (closed_form) = 1.472296417691134 y[1] (numeric) = 1.472296417691134 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.09 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] = 1.46 y[1] (closed_form) = 1.562291350412533 y[1] (numeric) = 1.562291350412533 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.09 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] = 1.55 y[1] (closed_form) = 1.652288397429258 y[1] (numeric) = 1.652288397429258 absolute error = 2.220446049250313e-16 relative error = 1.343861067296141e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.09 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] = 1.640000000000001 y[1] (closed_form) = 1.742286676571351 y[1] (numeric) = 1.742286676571351 absolute error = 4.440892098500626e-16 relative error = 2.548887136782717e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.09 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] = 1.730000000000001 y[1] (closed_form) = 1.832285673740316 y[1] (numeric) = 1.832285673740315 absolute error = 4.440892098500626e-16 relative error = 2.423689800201985e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.09 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] = 1.820000000000001 y[1] (closed_form) = 1.922285089340892 y[1] (numeric) = 1.922285089340891 absolute error = 6.661338147750939e-16 relative error = 3.465322695727179e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.09 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] = 1.910000000000001 y[1] (closed_form) = 2.012284748782676 y[1] (numeric) = 2.012284748782675 absolute error = 4.440892098500626e-16 relative error = 2.206890501549111e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.09 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 ) = tanh ( 3.0 * x + 1.0 ) ; 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 %