##############ECHO OF PROBLEM################# ##############temp/mult_sin_cpostode.ode################# diff ( y , x , 1 ) = sin ( x ) * 2.0 ; ! /* 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(glob__m1 *cos(c(x)) * c(2.0)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = -1.990008330556052 y[1] (numeric) = -1.990008330556052 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) = -1.960397084977247 y[1] (numeric) = -1.960397084977247 absolute error = 2.220446049250313e-16 relative error = 1.132651168615711e-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 = 0.1941 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) = -1.905517737852064 y[1] (numeric) = -1.905517737852064 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 = 0.2894 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) = -1.835882036170189 y[1] (numeric) = -1.835882036170189 absolute error = 4.440892098500626e-16 relative error = 2.418941964138784e-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) = -1.748145887610633 y[1] (numeric) = -1.748145887610634 absolute error = 8.881784197001252e-16 relative error = 5.080688207973809e-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) = -1.643174306082227 y[1] (numeric) = -1.643174306082227 absolute error = 4.440892098500626e-16 relative error = 2.702629953537259e-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) = -1.522002234188951 y[1] (numeric) = -1.522002234188951 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 = 0.4937 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) = -1.385824339456907 y[1] (numeric) = -1.385824339456907 absolute error = 4.440892098500626e-16 relative error = 3.204512990615372e-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) = -1.235983235790991 y[1] (numeric) = -1.23598323579099 absolute error = 8.881784197001252e-16 relative error = 7.186007010295076e-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) = -1.073956246289072 y[1] (numeric) = -1.07395624628907 absolute error = 1.554312234475219e-15 relative error = 1.447277056068122e-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) = -0.901340837922584 y[1] (numeric) = -0.9013408379225818 absolute error = 2.220446049250313e-15 relative error = 2.463492117330455e-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 = 0.4023 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) = -0.7198388716868688 y[1] (numeric) = -0.7198388716868657 absolute error = 3.108624468950438e-15 relative error = 4.318500418941943e-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) = -0.53123982350321 y[1] (numeric) = -0.5312398235032061 absolute error = 3.885780586188048e-15 relative error = 7.31455063094412e-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) = -0.3374031413021242 y[1] (numeric) = -0.3374031413021195 absolute error = 4.718447854656915e-15 relative error = 1.398459965857825e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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) = -0.1313877910009239 y[1] (numeric) = -0.1313877910009187 absolute error = 5.162537064506978e-15 relative error = 3.929236518232259e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 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] = 1.60002647828782 y[1] (closed_form) = 0.05845197857721707 y[1] (numeric) = 0.05845197857718205 absolute error = 3.502059753301978e-14 relative error = 5.991345098225608e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001642475171886937 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0303 Order of pole (three term test) = 33.52 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.700053216255798 y[1] (closed_form) = 0.2577945336025541 y[1] (numeric) = 0.2577945336023921 absolute error = 1.619815392928103e-13 relative error = 6.283358185652604e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001642475171886937 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 ) * 2.0 ; 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 = 32.74 %