##############ECHO OF PROBLEM################# ##############temp/sub_sin_cpostode.ode################# diff ( y , x , 1 ) = sin ( x ) - 1 , 0 ; ! /* 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); 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) - 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) = 0.9049958347219743 y[1] (numeric) = 0.9049958347219743 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) = 0.8204667921138458 y[1] (numeric) = 0.8204667921138458 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) = 0.7386383337391533 y[1] (numeric) = 0.7386383337391536 absolute error = 2.220446049250313e-16 relative error = 3.006134325590598e-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) = 0.6741215191825602 y[1] (numeric) = 0.6741215191825604 absolute error = 1.110223024625157e-16 relative error = 1.646918238081782e-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) = 0.6186549280648072 y[1] (numeric) = 0.6186549280648072 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 = 0.4246 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) = 0.5718060534314805 y[1] (numeric) = 0.5718060534314804 absolute error = 1.110223024625157e-16 relative error = 1.941607679671398e-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 = 0.4684 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) = 0.533057423980588 y[1] (numeric) = 0.5330574239805879 absolute error = 1.110223024625157e-16 relative error = 2.082745638048907e-14 % Desired digits = 8 Estimated correct digits = 12 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) = 0.5018117059490798 y[1] (numeric) = 0.5018117059490795 absolute error = 2.220446049250313e-16 relative error = 4.424859011709918e-14 % Desired digits = 8 Estimated correct digits = 12 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) = 0.4773975923845076 y[1] (numeric) = 0.4773975923845072 absolute error = 3.885780586188048e-16 relative error = 8.139506038937762e-14 % Desired digits = 8 Estimated correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = 1.003945455117527 y[1] (closed_form) = 0.4590764217379368 y[1] (numeric) = 0.4590764217379363 absolute error = 4.996003610813204e-16 relative error = 1.08827275247544e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.453 Order of pole (three term test) = 32.71 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.103280120515058 y[1] (closed_form) = 0.4460494605236505 y[1] (numeric) = 0.44604946052365 absolute error = 4.440892098500626e-16 relative error = 9.956053064803922e-14 % Desired digits = 8 Estimated correct digits = 12 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 = 0.4023 Order of pole (three term test) = 32.8 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.202614785912588 y[1] (closed_form) = 0.4374657782439779 y[1] (numeric) = 0.4374657782439774 absolute error = 5.551115123125783e-16 relative error = 1.268925570683128e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.3358 Order of pole (three term test) = 32.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.301949451310118 y[1] (closed_form) = 0.4324306369382771 y[1] (numeric) = 0.4324306369382765 absolute error = 6.106226635438361e-16 relative error = 1.412070772476265e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.2561 Order of pole (three term test) = 32.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.401284116707648 y[1] (closed_form) = 0.4300143126412896 y[1] (numeric) = 0.4300143126412891 absolute error = 4.996003610813204e-16 relative error = 1.161822633327273e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.1663 Order of pole (three term test) = 32.97 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) = 0.429251017600212 y[1] (numeric) = 0.4292510176002115 absolute error = 4.996003610813204e-16 relative error = 1.163888588719967e-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) = 33 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] = 1.599998651048332 y[1] (closed_form) = 0.4291995228764509 y[1] (numeric) = 0.4291995228764509 absolute error = 5.551115123125783e-17 relative error = 1.293364700389875e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0001474401342213636 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 , 1 ) = sin ( x ) - 1 , 0 ; 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 %