##############ECHO OF PROBLEM################# ##############temp/sqrt_sqrtpostode.ode################# diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=0.5; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=0.001; 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(0.8 * (x + 2.0) * sqrt(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 = 0.001 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 400 step_error = 1.25e-19 est_needed_step_err = 1.25e-19 opt_iter = 1 Radius of convergence (given) for eq 1 = 2.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.1 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.137271367855683 glob_desired_digits_correct = 16 estimated_h = 0.001 estimated_answer = 1.137271367855683 desired_abs_gbl_error = 1.137271367855683e-16 range = 0.4 estimated_steps = 400 step_error = 1.421589209819604e-19 est_needed_step_err = 1.421589209819604e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.387832209790197e-124 estimated_step_error = 2.387832209790197e-124 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 2.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.1 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.137271367855683 glob_desired_digits_correct = 16 estimated_h = 0.002 estimated_answer = 1.137271367855683 desired_abs_gbl_error = 1.137271367855683e-16 range = 0.4 estimated_steps = 200 step_error = 2.010430740650135e-19 est_needed_step_err = 2.010430740650135e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.640539030783244e-113 estimated_step_error = 1.640539030783244e-113 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 2.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.1 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.137271367855683 glob_desired_digits_correct = 16 estimated_h = 0.004 estimated_answer = 1.137271367855683 desired_abs_gbl_error = 1.137271367855683e-16 range = 0.4 estimated_steps = 100 step_error = 2.843178419639208e-19 est_needed_step_err = 2.843178419639208e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.126866092402042e-102 estimated_step_error = 1.126866092402042e-102 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 2.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.1 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.137271367855683 glob_desired_digits_correct = 16 estimated_h = 0.008 estimated_answer = 1.137271367855683 desired_abs_gbl_error = 1.137271367855683e-16 range = 0.4 estimated_steps = 50 step_error = 4.02086148130027e-19 est_needed_step_err = 4.02086148130027e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.736850689019475e-92 estimated_step_error = 7.736850689019475e-92 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 2.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.1 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.137271367855683 glob_desired_digits_correct = 16 estimated_h = 0.016 estimated_answer = 1.137271367855683 desired_abs_gbl_error = 1.137271367855683e-16 range = 0.4 estimated_steps = 25 step_error = 5.686356839278416e-19 est_needed_step_err = 5.686356839278416e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.307246047945901e-81 estimated_step_error = 5.307246047945901e-81 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 2.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.1 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.137271367855683 glob_desired_digits_correct = 16 estimated_h = 0.032 estimated_answer = 1.137271367855683 desired_abs_gbl_error = 1.137271367855683e-16 range = 0.4 estimated_steps = 12.5 step_error = 8.041722962600541e-19 est_needed_step_err = 8.041722962600541e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.634155780754282e-70 estimated_step_error = 3.634155780754282e-70 Double H and LOOP opt_iter = 7 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 2.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.313 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 1.137271367855683 y[1] (numeric) = 1.137271367855683 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.04 Radius of convergence (given) for eq 1 = 2.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.1 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (closed_form) = 1.164413424258851 y[1] (numeric) = 1.164413424258851 absolute error = 2.220446049250313e-16 relative error = 1.906922406587357e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.04 Radius of convergence (given) for eq 1 = 2.14 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.14 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (closed_form) = 1.191682615993191 y[1] (numeric) = 1.191682615993191 absolute error = 2.220446049250313e-16 relative error = 1.863286431681068e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.04 Radius of convergence (given) for eq 1 = 2.18 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.18 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (closed_form) = 1.219077189271908 y[1] (numeric) = 1.219077189271908 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.04 Radius of convergence (given) for eq 1 = 2.22 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.22 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (closed_form) = 1.246595445742095 y[1] (numeric) = 1.246595445742096 absolute error = 2.220446049250313e-16 relative error = 1.781208215411445e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.04 Radius of convergence (given) for eq 1 = 2.26 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.26 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (closed_form) = 1.274235739780027 y[1] (numeric) = 1.274235739780028 absolute error = 2.220446049250313e-16 relative error = 1.742570844570433e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.04 Radius of convergence (given) for eq 1 = 2.3 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.3 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (closed_form) = 1.301996475963283 y[1] (numeric) = 1.301996475963283 absolute error = 2.220446049250313e-16 relative error = 1.705416328110654e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.04 Radius of convergence (given) for eq 1 = 2.34 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.34 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3799999999999999 y[1] (closed_form) = 1.3298761067053 y[1] (numeric) = 1.3298761067053 absolute error = 2.220446049250313e-16 relative error = 1.669663841657668e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.04 Radius of convergence (given) for eq 1 = 2.38 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.38 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4199999999999999 y[1] (closed_form) = 1.357873130039368 y[1] (numeric) = 1.357873130039368 absolute error = 2.220446049250313e-16 relative error = 1.635238226700853e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.04 Radius of convergence (given) for eq 1 = 2.42 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.42 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4599999999999999 y[1] (closed_form) = 1.385986087540297 y[1] (numeric) = 1.385986087540297 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.04 Radius of convergence (given) for eq 1 = 2.46 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.46 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4999999999999999 y[1] (closed_form) = 1.414213562373095 y[1] (numeric) = 1.414213562373095 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.04 Radius of convergence (given) for eq 1 = 2.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.5 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 11 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 120 %