##############ECHO OF PROBLEM################# ##############temp/cos_sqrt_linpostode.ode################# diff ( y , x , 1 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=-1.4; x_end=-1.3; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.0001; glob_upper_ratio_limit=1.001; glob_lower_ratio_limit=0.999; glob_type_given_pole=1; array_given_rad_poles[1][1]=-1.5; 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(cos(sqrt(2.0*x+3.0))+sqrt(2.0*x+3.0)*sin(sqrt(2.0*x+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 = 0.09999999999999987 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 = 0.09967 Order of pole (three term test) = 1.64 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.095055278569961 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1.095055278569961 desired_abs_gbl_error = 1.095055278569961e-16 range = 0.09999999999999987 estimated_steps = 99999.99999999987 step_error = 1.154289614690417e-20 est_needed_step_err = 1.154289614690417e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.307033538337183e-137 estimated_step_error = 9.307033538337183e-137 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 = 0.09967 Order of pole (three term test) = 1.64 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.095055278569961 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1.095055278569961 desired_abs_gbl_error = 1.095055278569961e-16 range = 0.09999999999999987 estimated_steps = 49999.99999999993 step_error = 1.632412028001602e-20 est_needed_step_err = 1.632412028001602e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.245816212876361e-129 estimated_step_error = 6.245816212876361e-129 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 = 0.09967 Order of pole (three term test) = 1.64 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.095055278569961 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1.095055278569961 desired_abs_gbl_error = 1.095055278569961e-16 range = 0.09999999999999987 estimated_steps = 24999.99999999997 step_error = 2.308579229380834e-20 est_needed_step_err = 2.308579229380834e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.191458369448505e-121 estimated_step_error = 4.191458369448505e-121 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 = 0.09967 Order of pole (three term test) = 1.64 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.095055278569961 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1.095055278569961 desired_abs_gbl_error = 1.095055278569961e-16 range = 0.09999999999999987 estimated_steps = 12499.99999999998 step_error = 3.264824056003203e-20 est_needed_step_err = 3.264824056003203e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.81278917791049e-113 estimated_step_error = 2.81278917791049e-113 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 = 0.09967 Order of pole (three term test) = 1.64 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.095055278569961 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1.095055278569961 desired_abs_gbl_error = 1.095055278569961e-16 range = 0.09999999999999987 estimated_steps = 6249.999999999992 step_error = 4.617158458761667e-20 est_needed_step_err = 4.617158458761667e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.887562525600106e-105 estimated_step_error = 1.887562525600106e-105 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 = 0.09967 Order of pole (three term test) = 1.64 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.095055278569961 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1.095055278569961 desired_abs_gbl_error = 1.095055278569961e-16 range = 0.09999999999999987 estimated_steps = 3124.999999999996 step_error = 6.529648112006406e-20 est_needed_step_err = 6.529648112006406e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.26663005595734e-97 estimated_step_error = 1.26663005595734e-97 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 = 0.09967 Order of pole (three term test) = 1.64 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.095055278569961 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1.095055278569961 desired_abs_gbl_error = 1.095055278569961e-16 range = 0.09999999999999987 estimated_steps = 1562.499999999998 step_error = 9.234316917523335e-20 est_needed_step_err = 9.234316917523335e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.498979743554776e-90 estimated_step_error = 8.498979743554776e-90 Double H and LOOP opt_iter = 8 SETTING H FOR MAX H 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 = 0.07787 Order of pole (three term test) = 1.64 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = -1.4 y[1] (closed_form) = 1.095055278569961 y[1] (numeric) = 1.095055278569961 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.0001 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 = 0.09967 Order of pole (three term test) = 1.64 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.390000000000001 y[1] (closed_form) = 1.104023539025582 y[1] (numeric) = 1.10402402178796 absolute error = 4.827623780734314e-07 relative error = 4.372754393439116e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 0.11 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1096 Order of pole (three term test) = 1.64 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.380000000000002 y[1] (closed_form) = 1.112895425970474 y[1] (numeric) = 1.112896389858023 absolute error = 9.638875495543431e-07 relative error = 8.661079262805023e-05 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 0.12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1196 Order of pole (three term test) = 1.64 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.370000000000003 y[1] (closed_form) = 1.121671265134129 y[1] (numeric) = 1.12167270851403 absolute error = 1.443379900933905e-06 relative error = 0.0001286811872426193 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 6 h = 0.0001 Radius of convergence (given) for eq 1 = 0.13 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1296 Order of pole (three term test) = 1.64 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.360000000000004 y[1] (closed_form) = 1.130351381590728 y[1] (numeric) = 1.130353302834296 absolute error = 1.921243568681064e-06 relative error = 0.0001699687017657575 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 6 h = 0.0001 Radius of convergence (given) for eq 1 = 0.14 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1395 Order of pole (three term test) = 1.641 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.350000000000005 y[1] (closed_form) = 1.138936099760073 y[1] (numeric) = 1.138938497242578 absolute error = 2.397482505189785e-06 relative error = 0.0002105019329613696 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 6 h = 0.0001 Radius of convergence (given) for eq 1 = 0.15 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1495 Order of pole (three term test) = 1.641 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.340000000000007 y[1] (closed_form) = 1.147425743408531 y[1] (numeric) = 1.147428615509059 absolute error = 2.872100527850918e-06 relative error = 0.0002503081828475529 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 6 h = 0.0001 Radius of convergence (given) for eq 1 = 0.16 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1595 Order of pole (three term test) = 1.641 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.330000000000008 y[1] (closed_form) = 1.155820635649969 y[1] (numeric) = 1.155823980751316 absolute error = 3.345101346363677e-06 relative error = 0.0002894135338293711 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 6 h = 0.0001 Radius of convergence (given) for eq 1 = 0.17 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1694 Order of pole (three term test) = 1.641 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.320000000000009 y[1] (closed_form) = 1.164121098946692 y[1] (numeric) = 1.164124915435281 absolute error = 3.816488588936906e-06 relative error = 0.0003278429187813966 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 6 h = 0.0001 Radius of convergence (given) for eq 1 = 0.18 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1794 Order of pole (three term test) = 1.642 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.31000000000001 y[1] (closed_form) = 1.172327455110375 y[1] (numeric) = 1.172331741376194 absolute error = 4.286265819386514e-06 relative error = 0.00036562018578529 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 6 h = 0.0001 Radius of convergence (given) for eq 1 = 0.19 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1894 Order of pole (three term test) = 1.642 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.300000000000011 y[1] (closed_form) = 1.180440025302998 y[1] (numeric) = 1.180444779739545 absolute error = 4.754436546905438e-06 relative error = 0.0004027681580591152 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 6 h = 0.0001 Radius of convergence (given) for eq 1 = 0.2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1993 Order of pole (three term test) = 1.642 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations = 1001 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.2 %