##############ECHO OF PROBLEM################# ##############temp/h3sinpostode.ode################# diff ( y , x , 3 ) = 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(1.5); 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_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(1.0) + cos(c(x))); } double exact_soln_yp (double x) { return(glob__m1 * sin(c(x))); } double exact_soln_ypp (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) = 1.995004165278026 y[1] (numeric) = 1.995004165278026 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) = 1.980198542488623 y[1] (numeric) = 1.980198542488624 absolute error = 2.220446049250313e-16 relative error = 1.121324958890111e-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) = 32.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3086027973348146 y[1] (closed_form) = 1.952758868926032 y[1] (numeric) = 1.952758868926032 absolute error = 2.220446049250313e-16 relative error = 1.137081533508283e-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 = 0.2894 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) = 1.917941018085094 y[1] (numeric) = 1.917941018085095 absolute error = 2.220446049250313e-16 relative error = 1.157723844640043e-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) = 32.16 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5072721281298761 y[1] (closed_form) = 1.874072943805317 y[1] (numeric) = 1.874072943805317 absolute error = 4.440892098500626e-16 relative error = 2.369647410566297e-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) = 32.24 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6066067935274063 y[1] (closed_form) = 1.821587153041113 y[1] (numeric) = 1.821587153041113 absolute error = 2.220446049250313e-16 relative error = 1.218962290957812e-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) = 32.32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7059414589249365 y[1] (closed_form) = 1.761001117094475 y[1] (numeric) = 1.761001117094475 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 = 0.4937 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) = 1.692912169728453 y[1] (numeric) = 1.692912169728453 absolute error = 4.440892098500626e-16 relative error = 2.62322651931373e-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 = 0.4996 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) = 1.617991617895495 y[1] (numeric) = 1.617991617895495 absolute error = 4.440892098500626e-16 relative error = 2.744694131528844e-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 = 0.4859 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) = 1.536978123144536 y[1] (numeric) = 1.536978123144535 absolute error = 1.110223024625157e-15 relative error = 7.223414620591527e-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 = 0.453 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) = 1.450670418961292 y[1] (numeric) = 1.45067041896129 absolute error = 1.77635683940025e-15 relative error = 1.224507521613459e-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 = 0.4023 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) = 1.359919435843434 y[1] (numeric) = 1.359919435843432 absolute error = 2.220446049250313e-15 relative error = 1.632777641620492e-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) = 32.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.301949451310118 y[1] (closed_form) = 1.265619911751605 y[1] (numeric) = 1.265619911751602 absolute error = 2.886579864025407e-15 relative error = 2.280763629919831e-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) = 32.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.401284116707648 y[1] (closed_form) = 1.168701570651062 y[1] (numeric) = 1.168701570651058 absolute error = 3.774758283725532e-15 relative error = 3.2298735438703e-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) = 32.97 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 Finished! diff ( y , x , 3 ) = sin ( x ) ; Iterations = 142 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 100.9 %