##############ECHO OF PROBLEM################# ##############temp/add_c_sinpostode.ode################# diff ( y , x , 1 ) = 1.0 + sin ( 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(1.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=c(0.001); glob_type_given_pole=3; /* 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) - c(cos(c(x))) + 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) = 1.104995834721974 y[1] (numeric) = 1.104995834721974 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.05 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09933 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1993346653975308 y[1] (closed_form) = 1.219136122908907 y[1] (numeric) = 1.219136122908907 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1941 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3086027973348146 y[1] (closed_form) = 1.355843928408783 y[1] (numeric) = 1.355843928408782 absolute error = 6.661338147750939e-16 relative error = 4.913056737709244e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2894 Order of pole (three term test) = 32.09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4079374627323454 y[1] (closed_form) = 1.489996444647251 y[1] (numeric) = 1.48999644464725 absolute error = 4.440892098500626e-16 relative error = 2.980471607468825e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3642 Order of pole (three term test) = 32.16 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5072721281298761 y[1] (closed_form) = 1.633199184324559 y[1] (numeric) = 1.633199184324559 absolute error = 8.881784197001252e-16 relative error = 5.438273715936542e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4246 Order of pole (three term test) = 32.24 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6066067935274063 y[1] (closed_form) = 1.785019640486293 y[1] (numeric) = 1.785019640486293 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4684 Order of pole (three term test) = 32.32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7059414589249365 y[1] (closed_form) = 1.944940341830461 y[1] (numeric) = 1.944940341830462 absolute error = 4.440892098500626e-16 relative error = 2.28330504694099e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4937 Order of pole (three term test) = 32.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8052761243224668 y[1] (closed_form) = 2.112363954594013 y[1] (numeric) = 2.112363954594014 absolute error = 4.440892098500626e-16 relative error = 2.102332833715743e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4996 Order of pole (three term test) = 32.52 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.904610789719997 y[1] (closed_form) = 2.286619171824502 y[1] (numeric) = 2.286619171824503 absolute error = 8.881784197001252e-16 relative error = 3.884242862319065e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4859 Order of pole (three term test) = 32.62 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = 1.0 + sin ( x ) ; Iterations = 91 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 101.5 %