##############ECHO OF PROBLEM################# ##############temp/sqrt_sqrt_tzeropostode.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=0.0; 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 = 0.5 estimated_steps = 500 step_error = 1.118033988749895e-19 est_needed_step_err = 1.118033988749895e-19 opt_iter = 1 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.069984487962275 glob_desired_digits_correct = 16 estimated_h = 0.001 estimated_answer = 1.069984487962275 desired_abs_gbl_error = 1.069984487962275e-16 range = 0.5 estimated_steps = 500 step_error = 1.196279024976976e-19 est_needed_step_err = 1.196279024976976e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.301149185461061e-123 estimated_step_error = 1.301149185461061e-123 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.069984487962275 glob_desired_digits_correct = 16 estimated_h = 0.002 estimated_answer = 1.069984487962275 desired_abs_gbl_error = 1.069984487962275e-16 range = 0.5 estimated_steps = 250 step_error = 1.691794021504903e-19 est_needed_step_err = 1.691794021504903e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.939330682575976e-113 estimated_step_error = 8.939330682575976e-113 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.069984487962275 glob_desired_digits_correct = 16 estimated_h = 0.004 estimated_answer = 1.069984487962275 desired_abs_gbl_error = 1.069984487962275e-16 range = 0.5 estimated_steps = 125 step_error = 2.392558049953953e-19 est_needed_step_err = 2.392558049953953e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.140179234085203e-102 estimated_step_error = 6.140179234085203e-102 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.069984487962275 glob_desired_digits_correct = 16 estimated_h = 0.008 estimated_answer = 1.069984487962275 desired_abs_gbl_error = 1.069984487962275e-16 range = 0.5 estimated_steps = 62.5 step_error = 3.383588043009805e-19 est_needed_step_err = 3.383588043009805e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.215543581194522e-91 estimated_step_error = 4.215543581194522e-91 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.069984487962275 glob_desired_digits_correct = 16 estimated_h = 0.016 estimated_answer = 1.069984487962275 desired_abs_gbl_error = 1.069984487962275e-16 range = 0.5 estimated_steps = 31.25 step_error = 4.785116099907906e-19 est_needed_step_err = 4.785116099907906e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.891478434150864e-80 estimated_step_error = 2.891478434150864e-80 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.069984487962275 glob_desired_digits_correct = 16 estimated_h = 0.032 estimated_answer = 1.069984487962275 desired_abs_gbl_error = 1.069984487962275e-16 range = 0.5 estimated_steps = 15.625 step_error = 6.767176086019611e-19 est_needed_step_err = 6.767176086019611e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.97959994331525e-69 estimated_step_error = 1.97959994331525e-69 Double H and LOOP opt_iter = 7 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.562 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 y[1] (closed_form) = 1.069984487962275 y[1] (numeric) = 1.069984487962275 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.05 y[1] (closed_form) = 1.103525347863256 y[1] (numeric) = 1.103525347863256 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2.05 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.05 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 1.137271367855683 y[1] (numeric) = 1.137271367855683 absolute error = 2.220446049250313e-16 relative error = 1.952432912680241e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05 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] = 0.15 y[1] (closed_form) = 1.171218872736315 y[1] (numeric) = 1.171218872736315 absolute error = 2.220446049250313e-16 relative error = 1.895842101709556e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2.15 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.15 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (closed_form) = 1.205364337353195 y[1] (numeric) = 1.205364337353194 absolute error = 2.220446049250313e-16 relative error = 1.842136838166368e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2.2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.2 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (closed_form) = 1.239704377197174 y[1] (numeric) = 1.239704377197174 absolute error = 2.220446049250313e-16 relative error = 1.791109308067849e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2.25 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.25 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) = 1.274235739780027 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05 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] = 0.35 y[1] (closed_form) = 1.308955296717664 y[1] (numeric) = 1.308955296717664 absolute error = 2.220446049250313e-16 relative error = 1.696349794999343e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2.35 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.35 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (closed_form) = 1.343860036446944 y[1] (numeric) = 1.343860036446944 absolute error = 2.220446049250313e-16 relative error = 1.652289664867921e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2.4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.4 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (closed_form) = 1.378947057513221 y[1] (numeric) = 1.37894705751322 absolute error = 4.440892098500626e-16 relative error = 3.220494996022028e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2.45 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.45 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 = 4.440892098500626e-16 relative error = 3.14018491736755e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05 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 %