##############ECHO OF PROBLEM################# ##############temp/sub_lin_sinpostode.ode################# diff ( y , x , 1 ) = ( 0.1 * x + 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(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(cos(c(x)) + (c(0.05) * c(x) * 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) = 1.095504165278026 y[1] (numeric) = 1.095504165278026 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) = 1.181519923327611 y[1] (numeric) = 1.181519923327612 absolute error = 4.440892098500626e-16 relative error = 3.758626503726977e-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) = 1.26612345058699 y[1] (numeric) = 1.26612345058699 absolute error = 2.220446049250313e-16 relative error = 1.753735821116722e-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) = 1.334199129492465 y[1] (numeric) = 1.334199129492465 absolute error = 4.440892098500626e-16 relative error = 3.32850771697772e-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) = 1.394211322534064 y[1] (numeric) = 1.394211322534064 absolute error = 6.661338147750939e-16 relative error = 4.777854002536397e-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) = 1.4465925366662 y[1] (numeric) = 1.446592536666201 absolute error = 8.881784197001252e-16 relative error = 6.13979677889816e-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) = 1.491860243190865 y[1] (numeric) = 1.491860243190867 absolute error = 1.332267629550188e-15 relative error = 8.930244207732671e-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) = 1.530611775871111 y[1] (numeric) = 1.530611775871112 absolute error = 1.110223024625157e-15 relative error = 7.253459316901569e-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) = 1.563518441659384 y[1] (numeric) = 1.563518441659385 absolute error = 1.110223024625157e-15 relative error = 7.100799037885738e-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 TOP MAIN SOLVE Loop x[1] = 1.003945455117527 y[1] (closed_form) = 1.59131890210462 y[1] (numeric) = 1.591318902104621 absolute error = 1.110223024625157e-15 relative error = 6.976747546684804e-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 = 0.453 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) = 1.614811890692536 y[1] (numeric) = 1.614811890692537 absolute error = 1.332267629550188e-15 relative error = 8.250296131884597e-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) = 1.634848337920801 y[1] (numeric) = 1.634848337920803 absolute error = 1.554312234475219e-15 relative error = 9.507378748367524e-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 = 0.3358 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) = 1.652322981750059 y[1] (numeric) = 1.65232298175006 absolute error = 1.332267629550188e-15 relative error = 8.062997635844269e-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 = 0.2561 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) = 1.668165546145567 y[1] (numeric) = 1.668165546145569 absolute error = 1.554312234475219e-15 relative error = 9.31749392658651e-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 = 0.1663 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) = 1.684008523129865 y[1] (numeric) = 1.684008523129867 absolute error = 1.998401444325282e-15 relative error = 1.186693188827271e-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) = 1.698800261291373 y[1] (numeric) = 1.698800261291373 absolute error = 2.220446049250313e-16 relative error = 1.307067169604979e-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 ) = ( 0.1 * x + 1.0 ) - 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 %