##############ECHO OF PROBLEM################# ##############temp/sqrtpostode.ode################# diff ( y , x , 1 ) = sqrt ( x ) ; ! /* 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(0.2); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=c(0.001); glob_max_h=c(0.01); glob_type_given_pole=1; array_given_rad_poles[1][1]=c(0.0); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(1.5); 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(2.0)*expt(c(x),c(1.5))/c(3.0)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0.0210818510677892 y[1] (numeric) = 0.0210818510677892 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 SETTING H FOR POLE Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 1.5 Radius of convergence (ratio test) for eq 1 = 0.1077 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1999999999999993 y[1] (closed_form) = 0.05962847939999408 y[1] (numeric) = 0.05962847939999412 absolute error = 4.163336342344337e-17 relative error = 6.982127306007992e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009999999999999938 Radius of convergence (given) for eq 1 = 0.2 Order of pole (given) = 1.5 Radius of convergence (ratio test) for eq 1 = 0.2154 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.2 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sqrt ( x ) ; 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 %