##############ECHO OF PROBLEM################# ##############temp/arccos_sqrtpostode.ode################# diff ( y , x , 1 ) = arccos ( 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(0.001); 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(10.0) * (c(0.1) * c(x) + c(0.2)) * arccos(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) = 2.532535480592211 y[1] (numeric) = 2.532535480592211 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) = 2.642629173205489 y[1] (numeric) = 2.642629497017106 absolute error = 3.238116175197092e-07 relative error = 1.225338843614325e-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) = 2.751495138739343 y[1] (numeric) = 2.751495784793056 absolute error = 6.460537131935951e-07 relative error = 2.348009647909458e-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) = 2.859153953861397 y[1] (numeric) = 2.859154921020775 absolute error = 9.671593788063149e-07 relative error = 3.382676814237754e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 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) = 2.965624522830128 y[1] (numeric) = 2.965625810359106 absolute error = 1.287528977655938e-06 relative error = 4.341510422995947e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 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) = 3.070924246521893 y[1] (numeric) = 3.070925854057727 absolute error = 1.607535833780815e-06 relative error = 5.23469712937888e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 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 ) = arccos ( 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 %