##############ECHO OF PROBLEM################# ##############temp/h2sinpostode.ode################# diff ( y , x , 2 ) = 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(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); array_y_init[1 + 1] = exact_soln_yp(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=(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) - sin(c(x))); } double exact_soln_yp (double x) { return(glob__m1 * 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) = 1.900166583353172 y[1] (numeric) = 1.900166583353172 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) = 32.99 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1993346653975308 y[1] (closed_form) = 1.801982785336279 y[1] (numeric) = 1.801982785336279 absolute error = 2.220446049250313e-16 relative error = 1.232223785554057e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753069 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) = 32.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3086027973348146 y[1] (closed_form) = 1.696272263889535 y[1] (numeric) = 1.696272263889535 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753069 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) = 32.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4079374627323454 y[1] (closed_form) = 1.603283114404113 y[1] (numeric) = 1.603283114404112 absolute error = 2.220446049250313e-16 relative error = 1.384936964221431e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753069 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) = 32.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5072721281298761 y[1] (closed_form) = 1.514205301688555 y[1] (numeric) = 1.514205301688555 absolute error = 2.220446049250313e-16 relative error = 1.466410166953053e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753069 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) = 32.76 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6066067935274063 y[1] (closed_form) = 1.429917067473689 y[1] (numeric) = 1.429917067473689 absolute error = 4.440892098500626e-16 relative error = 3.105699064314679e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753069 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) = 32.68 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7059414589249365 y[1] (closed_form) = 1.351249431768295 y[1] (numeric) = 1.351249431768294 absolute error = 1.110223024625157e-15 relative error = 8.216270057351867e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753069 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) = 32.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8052761243224668 y[1] (closed_form) = 1.278977999612906 y[1] (numeric) = 1.278977999612904 absolute error = 1.332267629550188e-15 relative error = 1.041665790931049e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.009933466539753069 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) = 32.48 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.904610789719997 y[1] (closed_form) = 1.213815314184442 y[1] (numeric) = 1.213815314184441 absolute error = 1.332267629550188e-15 relative error = 1.097586769569911e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.009933466539753069 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) = 32.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.003945455117527 y[1] (closed_form) = 1.156403831644446 y[1] (numeric) = 1.156403831644445 absolute error = 1.332267629550188e-15 relative error = 1.152078186783294e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.009933466539753069 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.453 Order of pole (three term test) = 32.29 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.103280120515058 y[1] (closed_form) = 1.107309586993759 y[1] (numeric) = 1.107309586993757 absolute error = 1.77635683940025e-15 relative error = 1.60420975332011e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.009933466539753069 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4023 Order of pole (three term test) = 32.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.202614785912588 y[1] (closed_form) = 1.067016613383634 y[1] (numeric) = 1.067016613383632 absolute error = 2.220446049250313e-15 relative error = 2.080985451771946e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.009933466539753069 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3358 Order of pole (three term test) = 32.13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.301949451310118 y[1] (closed_form) = 1.0359221699048 y[1] (numeric) = 1.035922169904798 absolute error = 1.998401444325282e-15 relative error = 1.929103848128796e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.009933466539753069 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2561 Order of pole (three term test) = 32.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.401284116707648 y[1] (closed_form) = 1.014332824904946 y[1] (numeric) = 1.014332824904943 absolute error = 2.220446049250313e-15 relative error = 2.189070485280207e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.009933466539753069 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1663 Order of pole (three term test) = 32.03 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 1.505055086899326 y[1] (closed_form) = 1.002160177135641 y[1] (numeric) = 1.00216017713564 absolute error = 1.77635683940025e-15 relative error = 1.772527865233486e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.007275776712777522 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 = 0.06555 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 1.600025180122412 y[1] (closed_form) = 1.000427132522925 y[1] (numeric) = 1.000427132522923 absolute error = 1.77635683940025e-15 relative error = 1.775598423565892e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001475676775900672 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 2 ) = sin ( x ) ; Iterations = 1000 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Expected Time Remaining = 0.0 Seconds Optimized Time Remaining = 0.0 Seconds Expected Total Time = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 32.46 %