##############ECHO OF PROBLEM################# ##############temp/h5h3postode.ode################# diff ( y , x , 5 ) = neg ( diff ( y , x , 3 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=64; 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); array_y_init[1 + 1] = exact_soln_yp(x_start); array_y_init[2 + 1] = exact_soln_ypp(x_start); array_y_init[3 + 1] = exact_soln_yppp(x_start); array_y_init[4 + 1] = exact_soln_ypppp(x_start); glob_look_poles=true; glob_type_given_pole=3; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(cos(c(x))); } double exact_soln_yp (double x) { return(neg(sin(c(x)))); } double exact_soln_ypp (double x) { return(neg(cos(c(x)))); } double exact_soln_yppp (double x) { return(sin(x)); } double exact_soln_ypppp (double x) { return(cos(c(x))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0.9950041652780258 y[1] (numeric) = 0.9950041652780258 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (closed_form) = 0.9939560979566968 y[1] (numeric) = 0.9939560979566969 absolute error = 1.110223024625157e-16 relative error = 1.116973905494893e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (closed_form) = 0.9928086358538663 y[1] (numeric) = 0.9928086358538663 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = 0.9915618937147881 y[1] (numeric) = 0.9915618937147881 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (closed_form) = 0.9902159962126371 y[1] (numeric) = 0.9902159962126372 absolute error = 1.110223024625157e-16 relative error = 1.121192779021467e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = 0.9887710779360422 y[1] (numeric) = 0.9887710779360421 absolute error = 1.110223024625157e-16 relative error = 1.122831208759294e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (closed_form) = 0.9872272833756269 y[1] (numeric) = 0.9872272833756267 absolute error = 2.220446049250313e-16 relative error = 2.249174112832397e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (closed_form) = 0.9855847669095607 y[1] (numeric) = 0.9855847669095603 absolute error = 3.33066907387547e-16 relative error = 3.379383677285567e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (closed_form) = 0.9838436927881214 y[1] (numeric) = 0.9838436927881212 absolute error = 2.220446049250313e-16 relative error = 2.256909370387664e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (closed_form) = 0.9820042351172703 y[1] (numeric) = 0.9820042351172701 absolute error = 2.220446049250313e-16 relative error = 2.261136937953377e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 Finished! diff ( y , x , 5 ) = neg ( diff ( y , x , 3 ) ) ; Iterations = 100 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 101 %