##############ECHO OF PROBLEM################# ##############temp/arcsin_sqrtpostode.ode################# diff ( y , x , 1 ) = arcsin ( sqrt ( 0.1 * x + 0.2 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.0); x_end=c(0.5); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=c(0.01); 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(10.0) * (c(0.1) * c(x) + c(0.2)) * arcsin(sqrt ( c(0.1) * c(x) + c(0.2))) + c(5.0) * sqrt( c(0.1) * c(x) + c(0.2)) * sqrt( c(0.8) - c(0.1) * c(x)) - c(5.0) * arcsin(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 y[1] (closed_form) = 0.609057172997582 y[1] (numeric) = 0.609057172997582 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 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 2.222 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0.6560431130637943 y[1] (numeric) = 0.6560427892521767 absolute error = 3.238116175197092e-07 relative error = 4.935828317859675e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 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 = 2.333 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.1 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (closed_form) = 0.7042567802094295 y[1] (numeric) = 0.7042561341557165 absolute error = 6.460537129715505e-07 relative error = 9.173553327799403e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 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 = 2.444 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (closed_form) = 0.7536775977668664 y[1] (numeric) = 0.7536766306074867 absolute error = 9.671593796944933e-07 relative error = 0.0001283253452882466 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 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 = 2.555 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.3 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (closed_form) = 0.8042866614776245 y[1] (numeric) = 0.8042853739486457 absolute error = 1.287528978766161e-06 relative error = 0.0001600833434686994 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 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 = 2.666 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.4 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4999999999999999 y[1] (closed_form) = 0.856066570465349 y[1] (numeric) = 0.8560649629295144 absolute error = 1.607535834557972e-06 relative error = 0.0001877816387204714 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 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 = 2.777 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.5 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = arcsin ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 11 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 120 %