##############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=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(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 = 10 estimated_h = 0.001 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 500 step_error = 1.118033988749895e-13 est_needed_step_err = 1.118033988749895e-13 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 = 10 estimated_h = 0.001 estimated_answer = 1.069984487962275 desired_abs_gbl_error = 1.069984487962275e-10 range = 0.5 estimated_steps = 500 step_error = 1.196279024976976e-13 est_needed_step_err = 1.196279024976976e-13 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 = 10 estimated_h = 0.002 estimated_answer = 1.069984487962275 desired_abs_gbl_error = 1.069984487962275e-10 range = 0.5 estimated_steps = 250 step_error = 1.691794021504903e-13 est_needed_step_err = 1.691794021504903e-13 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 = 10 estimated_h = 0.004 estimated_answer = 1.069984487962275 desired_abs_gbl_error = 1.069984487962275e-10 range = 0.5 estimated_steps = 125 step_error = 2.392558049953952e-13 est_needed_step_err = 2.392558049953952e-13 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 = 10 estimated_h = 0.008 estimated_answer = 1.069984487962275 desired_abs_gbl_error = 1.069984487962275e-10 range = 0.5 estimated_steps = 62.5 step_error = 3.383588043009805e-13 est_needed_step_err = 3.383588043009805e-13 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 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 = 1.25 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] (analytic) = 1.069984487962275 y[1] (numeric) = 1.069984487962275 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.01 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] = 0.01 y[1] (analytic) = 1.076676065425809 y[1] (numeric) = 1.076676065425809 absolute error = 2.220446049250313e-16 relative error = 2.062315788892512e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.01 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.01 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.02 y[1] (analytic) = 1.083375970955018 y[1] (numeric) = 1.083375970955018 absolute error = 2.220446049250313e-16 relative error = 2.049561840745779e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.02 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.02 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.03 y[1] (analytic) = 1.09008417360947 y[1] (numeric) = 1.090084173609471 absolute error = 2.220446049250313e-16 relative error = 2.036949166868468e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.03 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.03 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.04 y[1] (analytic) = 1.09680064271563 y[1] (numeric) = 1.09680064271563 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.04 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.04 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] (analytic) = 1.103525347863256 y[1] (numeric) = 1.103525347863256 absolute error = 2.220446049250313e-16 relative error = 2.012138691285831e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 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] = 0.06 y[1] (analytic) = 1.110258258901869 y[1] (numeric) = 1.110258258901869 absolute error = 2.220446049250313e-16 relative error = 1.999936529584122e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.06 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.06 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.07000000000000001 y[1] (analytic) = 1.116999345937281 y[1] (numeric) = 1.116999345937281 absolute error = 2.220446049250313e-16 relative error = 1.98786691982091e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.07 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.07 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.08 y[1] (analytic) = 1.123748579328188 y[1] (numeric) = 1.123748579328189 absolute error = 2.220446049250313e-16 relative error = 1.975927792120338e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.08 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.08 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09 y[1] (analytic) = 1.130505929682826 y[1] (numeric) = 1.130505929682826 absolute error = 4.440892098500626e-16 relative error = 3.928234237344124e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.09 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.09 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09999999999999999 y[1] (analytic) = 1.137271367855683 y[1] (numeric) = 1.137271367855683 absolute error = 2.220446049250313e-16 relative error = 1.952432912680241e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 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] = 0.11 y[1] (analytic) = 1.144044864944275 y[1] (numeric) = 1.144044864944275 absolute error = 2.220446049250313e-16 relative error = 1.940873227343639e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.11 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.11 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 1.150826392285975 y[1] (numeric) = 1.150826392285975 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.12 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 1.157615921454899 y[1] (numeric) = 1.157615921454899 absolute error = 2.220446049250313e-16 relative error = 1.918119825494144e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.13 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.13 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] (analytic) = 1.164413424258851 y[1] (numeric) = 1.164413424258851 absolute error = 2.220446049250313e-16 relative error = 1.906922406587357e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 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] = 0.15 y[1] (analytic) = 1.171218872736315 y[1] (numeric) = 1.171218872736315 absolute error = 2.220446049250313e-16 relative error = 1.895842101709556e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 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] = 0.16 y[1] (analytic) = 1.178032239153504 y[1] (numeric) = 1.178032239153504 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.16 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.16 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 1.184853496001456 y[1] (numeric) = 1.184853496001457 absolute error = 2.220446049250313e-16 relative error = 1.874025824073345e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.17 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.17 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] (analytic) = 1.191682615993191 y[1] (numeric) = 1.191682615993191 absolute error = 2.220446049250313e-16 relative error = 1.863286431681068e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 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] = 0.19 y[1] (analytic) = 1.198519572060899 y[1] (numeric) = 1.1985195720609 absolute error = 2.220446049250313e-16 relative error = 1.852657312414325e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.19 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.19 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] (analytic) = 1.205364337353195 y[1] (numeric) = 1.205364337353195 absolute error = 2.220446049250313e-16 relative error = 1.842136838166368e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 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] = 0.21 y[1] (analytic) = 1.212216885232404 y[1] (numeric) = 1.212216885232404 absolute error = 4.440892098500626e-16 relative error = 3.663446824244844e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.21 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.21 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y[1] (analytic) = 1.219077189271908 y[1] (numeric) = 1.219077189271909 absolute error = 2.220446049250313e-16 relative error = 1.821415468020093e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 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] = 0.2300000000000001 y[1] (analytic) = 1.225945223253526 y[1] (numeric) = 1.225945223253526 absolute error = 2.220446049250313e-16 relative error = 1.811211469430493e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.23 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.23 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y[1] (analytic) = 1.232820961164941 y[1] (numeric) = 1.232820961164941 absolute error = 2.220446049250313e-16 relative error = 1.801109909059403e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.24 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.24 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y[1] (analytic) = 1.239704377197174 y[1] (numeric) = 1.239704377197174 absolute error = 2.220446049250313e-16 relative error = 1.791109308067849e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 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] = 0.2600000000000001 y[1] (analytic) = 1.246595445742096 y[1] (numeric) = 1.246595445742096 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 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] = 0.2700000000000001 y[1] (analytic) = 1.253494141389982 y[1] (numeric) = 1.253494141389982 absolute error = 2.220446049250313e-16 relative error = 1.771405207197931e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.27 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.27 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (analytic) = 1.260400438927108 y[1] (numeric) = 1.260400438927108 absolute error = 2.220446049250313e-16 relative error = 1.761698886062295e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.28 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.28 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (analytic) = 1.267314313333384 y[1] (numeric) = 1.267314313333384 absolute error = 2.220446049250313e-16 relative error = 1.752087880558952e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.29 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.29 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3000000000000001 y[1] (analytic) = 1.274235739780028 y[1] (numeric) = 1.274235739780028 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 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] = 0.3100000000000001 y[1] (analytic) = 1.281164693627276 y[1] (numeric) = 1.281164693627276 absolute error = 2.220446049250313e-16 relative error = 1.733146456732048e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.31 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.31 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3200000000000001 y[1] (analytic) = 1.288101150422135 y[1] (numeric) = 1.288101150422135 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.32 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.32 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3300000000000001 y[1] (analytic) = 1.29504508589616 y[1] (numeric) = 1.29504508589616 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.33 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.33 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3400000000000001 y[1] (analytic) = 1.301996475963283 y[1] (numeric) = 1.301996475963283 absolute error = 2.220446049250313e-16 relative error = 1.705416328110653e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 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] = 0.3500000000000001 y[1] (analytic) = 1.308955296717664 y[1] (numeric) = 1.308955296717664 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 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] = 0.3600000000000002 y[1] (analytic) = 1.315921524431581 y[1] (numeric) = 1.315921524431581 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.36 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.36 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y[1] (analytic) = 1.322895135553353 y[1] (numeric) = 1.322895135553353 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.37 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.37 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y[1] (analytic) = 1.3298761067053 y[1] (numeric) = 1.3298761067053 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 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] = 0.3900000000000002 y[1] (analytic) = 1.336864414681727 y[1] (numeric) = 1.336864414681727 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.39 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.39 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y[1] (analytic) = 1.343860036446944 y[1] (numeric) = 1.343860036446944 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 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] = 0.4100000000000002 y[1] (analytic) = 1.350862949133322 y[1] (numeric) = 1.350862949133322 absolute error = 2.220446049250313e-16 relative error = 1.643724147349583e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.41 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.41 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4200000000000002 y[1] (analytic) = 1.357873130039369 y[1] (numeric) = 1.357873130039369 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 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] = 0.4300000000000002 y[1] (analytic) = 1.364890556627842 y[1] (numeric) = 1.364890556627842 absolute error = 2.220446049250313e-16 relative error = 1.626830838903483e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.43 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.43 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4400000000000002 y[1] (analytic) = 1.37191520652389 y[1] (numeric) = 1.37191520652389 absolute error = 2.220446049250313e-16 relative error = 1.618500938462808e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.44 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.44 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4500000000000002 y[1] (analytic) = 1.378947057513221 y[1] (numeric) = 1.378947057513221 absolute error = 2.220446049250313e-16 relative error = 1.610247498011014e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 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] = 0.4600000000000002 y[1] (analytic) = 1.385986087540297 y[1] (numeric) = 1.385986087540297 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 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] = 0.4700000000000003 y[1] (analytic) = 1.393032274706562 y[1] (numeric) = 1.393032274706562 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.47 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.47 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y[1] (analytic) = 1.400085597268692 y[1] (numeric) = 1.400085597268692 absolute error = 2.220446049250313e-16 relative error = 1.585935926761901e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.48 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.48 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (analytic) = 1.40714603363687 y[1] (numeric) = 1.407146033636871 absolute error = 2.220446049250313e-16 relative error = 1.57797840179488e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.49 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.49 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 = 50 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 102 %