##############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=0.000005; glob_upper_ratio_limit=1.001; glob_lower_ratio_limit=0.999; glob_min_h=0.000001; 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=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=100000000; glob_max_minutes=10.0; glob_subiter_method=3; /* 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 = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.09999999999999987 estimated_steps = 99999.99999999987 step_error = 1.05409255338946e-14 est_needed_step_err = 1.05409255338946e-14 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 = 10 estimated_h = 1e-06 estimated_answer = 1.095055278569961 desired_abs_gbl_error = 1.095055278569961e-10 range = 0.09999999999999987 estimated_steps = 99999.99999999987 step_error = 1.154289614690417e-14 est_needed_step_err = 1.154289614690417e-14 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 = 10 estimated_h = 2e-06 estimated_answer = 1.095055278569961 desired_abs_gbl_error = 1.095055278569961e-10 range = 0.09999999999999987 estimated_steps = 49999.99999999993 step_error = 1.632412028001602e-14 est_needed_step_err = 1.632412028001602e-14 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 = 10 estimated_h = 4e-06 estimated_answer = 1.095055278569961 desired_abs_gbl_error = 1.095055278569961e-10 range = 0.09999999999999987 estimated_steps = 24999.99999999997 step_error = 2.308579229380834e-14 est_needed_step_err = 2.308579229380834e-14 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 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 = 0.06229 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] (analytic) = 1.095055278569961 y[1] (numeric) = 1.095055278569961 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 5e-06 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] = -1.389999999999934 y[1] (analytic) = 1.104023539025641 y[1] (numeric) = 1.104023563159928 absolute error = 2.4134287013311e-08 relative error = 2.186030112601655e-06 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 8 h = 5e-06 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] = -1.379999999999869 y[1] (analytic) = 1.112895425970591 y[1] (numeric) = 1.112895474157634 absolute error = 4.818704346654101e-08 relative error = 4.32988062867772e-06 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 8 h = 5e-06 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] = -1.369999999999803 y[1] (analytic) = 1.121671265134304 y[1] (numeric) = 1.121671337292736 absolute error = 7.215843278451928e-08 relative error = 6.433117708144138e-06 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 8 h = 5e-06 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] = -1.359999999999738 y[1] (analytic) = 1.130351381590958 y[1] (numeric) = 1.130351477639587 absolute error = 9.604862949430526e-08 relative error = 8.497236439797845e-06 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 8 h = 5e-06 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] = -1.349999999999672 y[1] (analytic) = 1.138936099760357 y[1] (numeric) = 1.138936219618151 absolute error = 1.198577939121037e-07 relative error = 1.052366273554091e-05 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 7 h = 5e-06 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] = -1.339999999999607 y[1] (analytic) = 1.147425743408868 y[1] (numeric) = 1.147425886994954 absolute error = 1.435860861320748e-07 relative error = 1.251375846819484e-05 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 7 h = 5e-06 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] = -1.329999999999541 y[1] (analytic) = 1.155820635650358 y[1] (numeric) = 1.155820802884031 absolute error = 1.672336729097168e-07 relative error = 1.44688256768852e-05 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 7 h = 5e-06 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] = -1.319999999999476 y[1] (analytic) = 1.164121098947132 y[1] (numeric) = 1.164121289747854 absolute error = 1.908007218887064e-07 relative error = 1.639010941913798e-05 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 7 h = 5e-06 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] = -1.30999999999941 y[1] (analytic) = 1.172327455110864 y[1] (numeric) = 1.172327669398262 absolute error = 2.142873980481852e-07 relative error = 1.827880061274523e-05 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 7 h = 5e-06 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 Finished! diff ( y , x , 1 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations = 20000 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 100 %