##############ECHO OF PROBLEM################# ##############temp/sp_diff2_2postode.ode################# diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-1.0; x_end=-0.99; 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); glob_look_poles=true; glob_max_iter=1000000000; glob_display_interval=0.001; glob_max_minutes=2; glob_desired_digits_correct=10; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return( - cos(x)); } double exact_soln_yp (double x) { return( sin(x)); } double exact_soln_ypp (double x) { return( cos(x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 opt_iter = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 0.01000000000000001 estimated_steps = 10.00000000000001 step_error = 9.999999999999991e-12 est_needed_step_err = 9.999999999999991e-12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 7.161023933293401e-36 max_value3 = 7.161023933293401e-36 value3 = 7.161023933293401e-36 best_h = 0.001 START of Soultion x[1] = -1 y[1] (analytic) = -0.5403023058681398 y[1] (numeric) = -0.5403023058681398 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.999 y[1] (analytic) = -0.5411435065615721 y[1] (numeric) = -0.5411435065615721 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.998 y[1] (analytic) = -0.5419841661115429 y[1] (numeric) = -0.5419841661115429 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.997 y[1] (analytic) = -0.5428242836773928 y[1] (numeric) = -0.5428242836773923 absolute error = 4.440892098500626e-16 relative error = 8.181085909450403e-14 % Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.996 y[1] (analytic) = -0.5436638584190042 y[1] (numeric) = -0.543663858419002 absolute error = 2.220446049250313e-15 relative error = 4.084225969530984e-13 % Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.995 y[1] (analytic) = -0.5445028894968026 y[1] (numeric) = -0.5445028894967955 absolute error = 7.105427357601002e-15 relative error = 1.304938411652401e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.994 y[1] (analytic) = -0.5453413760717568 y[1] (numeric) = -0.5453413760717388 absolute error = 1.798561299892754e-14 relative error = 3.298046652627539e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.993 y[1] (analytic) = -0.5461793173053804 y[1] (numeric) = -0.5461793173053413 absolute error = 3.907985046680551e-14 relative error = 7.155131882256014e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.992 y[1] (analytic) = -0.5470167123597323 y[1] (numeric) = -0.5470167123596559 absolute error = 7.638334409421077e-14 relative error = 1.396362165329587e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.991 y[1] (analytic) = -0.5478535603974173 y[1] (numeric) = -0.5478535603972795 absolute error = 1.377786773559819e-13 relative error = 2.514881481395068e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = -0.99 y[1] (analytic) = -0.5486898605815875 y[1] (numeric) = -0.5486898605813542 absolute error = 2.333688797762079e-13 relative error = 4.253201973312337e-11 % Correct digits = 12 h = 0.001 Finished! diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ; Iterations = 10 Total Elapsed Time = 0 Seconds Elapsed Time(since restart) = 0 Seconds Time to Timeout = 2 Minutes 0 Seconds Percent Done = 110 %