##############ECHO OF PROBLEM################# ##############temp/sqrt_sqrt_tonepostode.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(0.5); x_end=c(1.5); 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] = 0.5 y[1] (closed_form) = 1.414213562373095 y[1] (numeric) = 1.414213562373095 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 = 2.5 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 TOP MAIN SOLVE Loop x[1] = 0.6000000000000001 y[1] (closed_form) = 1.485274318892232 y[1] (numeric) = 1.485274318892232 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 = 2.6 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 2.779 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.6 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7000000000000002 y[1] (closed_form) = 1.557021796359321 y[1] (numeric) = 1.557021796359321 absolute error = 2.220446049250313e-16 relative error = 1.42608539870298e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2.7 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 2.885 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.7 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8000000000000003 y[1] (closed_form) = 1.62943682162873 y[1] (numeric) = 1.62943682162873 absolute error = 2.220446049250313e-16 relative error = 1.362707666708323e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2.8 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 2.992 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.8 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9000000000000004 y[1] (closed_form) = 1.702501426076371 y[1] (numeric) = 1.702501426076371 absolute error = 2.220446049250313e-16 relative error = 1.304225661864854e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2.9 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 3.099 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.9 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = 1.776198730781485 y[1] (numeric) = 1.776198730781485 absolute error = 2.220446049250313e-16 relative error = 1.250111268953204e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 3 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 3.206 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.100000000000001 y[1] (closed_form) = 1.850512846136167 y[1] (numeric) = 1.850512846136167 absolute error = 2.220446049250313e-16 relative error = 1.199908476121395e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 3.1 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 3.313 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.1 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.200000000000001 y[1] (closed_form) = 1.925428783660234 y[1] (numeric) = 1.925428783660234 absolute error = 4.440892098500626e-16 relative error = 2.3064431861554e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 3.2 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 3.42 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.2 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.300000000000001 y[1] (closed_form) = 2.000932378200509 y[1] (numeric) = 2.000932378200509 absolute error = 4.440892098500626e-16 relative error = 2.219411383854179e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 3.3 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 3.527 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.3 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.400000000000001 y[1] (closed_form) = 2.077010219012499 y[1] (numeric) = 2.077010219012498 absolute error = 4.440892098500626e-16 relative error = 2.138117597039084e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 3.634 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.4 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 = 20 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 105 %