##############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=c(0.1); x_end=c(0.5); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=c(0.001); glob_type_given_pole=1; array_given_rad_poles[1][1]=c(-2.0); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(0.5); array_given_ord_poles[1][2]=c(0.0); /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(20.0); glob_subiter_method=3; glob_max_iter=1000; glob_upper_ratio_limit=c(1.11); glob_lower_ratio_limit=c(0.99); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(c(0.8) * (c(x) + c(2.0)) * sqrt(sqrt(c(0.1) * c(x) + c(0.2)))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# 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 = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2.1 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 2.244 Order of pole (ratio test) = 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] = 0.2 y[1] (closed_form) = 1.205364337353195 y[1] (numeric) = 1.205364337353195 absolute error = 0 relative error = 0 % Desired digits = 8 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 Radius of convergence (ratio test) for eq 1 = 2.351 Order of pole (ratio test) = 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] = 0.3 y[1] (closed_form) = 1.274235739780027 y[1] (numeric) = 1.274235739780028 absolute error = 2.220446049250313e-16 relative error = 1.742570844570433e-14 % Desired digits = 8 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 Radius of convergence (ratio test) for eq 1 = 2.458 Order of pole (ratio test) = 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] = 0.4 y[1] (closed_form) = 1.343860036446944 y[1] (numeric) = 1.343860036446944 absolute error = 0 relative error = 0 % Desired digits = 8 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 Radius of convergence (ratio test) for eq 1 = 2.565 Order of pole (ratio test) = 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] = 0.4999999999999999 y[1] (closed_form) = 1.414213562373095 y[1] (numeric) = 1.414213562373095 absolute error = 2.220446049250313e-16 relative error = 1.570092458683775e-14 % Desired digits = 8 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 Radius of convergence (ratio test) for eq 1 = 2.672 Order of pole (ratio test) = 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 = 9 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 125 %