##############ECHO OF PROBLEM################# ##############temp/mtest8postode.ode################# diff ( y2 , x , 4 ) = y1 - 1.0 ; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ; ! /* 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(1.4); array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); array_y2_init[1 + 1] = exact_soln_y2p(x_start); array_y2_init[2 + 1] = exact_soln_y2pp(x_start); array_y2_init[3 + 1] = exact_soln_y2ppp(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_y1 (double x) { return(c(1.0) + sin(c(x))); } double exact_soln_y2 (double x) { return(c(1.0) + sin(c(x))); } double exact_soln_y2p (double x) { return( cos(c(x))); } double exact_soln_y2pp (double x) { return(glob__m1 * sin(c(x))); } double exact_soln_y2ppp (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 y2[1] (closed_form) = 1.099833416646828 y2[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 y1[1] (closed_form) = 1.099833416646828 y1[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 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 = 0.009175 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.009175 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 2 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] = 0.2000233743936064 y2[1] (closed_form) = 1.198692239202737 y2[1] (numeric) = 1.198691823691997 absolute error = 4.155107404812952e-07 relative error = 3.466367153237396e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 9.705024911334469e-05 y1[1] (closed_form) = 1.198692239202737 y1[1] (numeric) = 0.9210035645032596 absolute error = 0.2776886746994777 relative error = 23.16596918022689 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 2 h = 9.705024911334469e-05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04902 Order of pole (three term test) = 31.32 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.04902 Order of pole (three term test) = 31.32 NO COMPLEX POLE (six term test) for Equation 2 Finished! Maximum Iterations Reached before Solution Completed! diff ( y2 , x , 4 ) = y1 - 1.0 ; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ; Iterations = 1000 Total Elapsed Time = 1.0 Seconds Elapsed Time(since restart) = 1.0 Seconds Expected Time Remaining = 7.2 Seconds Optimized Time Remaining = 7.2 Seconds Expected Total Time = 8.2 Seconds Time to Timeout = 19 Minutes 59.0 Seconds Percent Done = 12.17 %