##############ECHO OF PROBLEM################# ##############temp/diff2postode.ode################# diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(-1.0); x_end=c(1.0); 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( glob__m1 * cos(c(x))); } double exact_soln_yp (double x) { return( sin(c(x))); } double exact_soln_ypp (double x) { return( cos(c(x))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -1 y[1] (closed_form) = -0.5403023058681398 y[1] (numeric) = -0.5403023058681398 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 = 0.06234 Order of pole (three term test) = 33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9002480934222241 y[1] (closed_form) = -0.6214156108887741 y[1] (numeric) = -0.6214436248365511 absolute error = 2.801394777707245e-05 relative error = 0.004508085617129211 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 5 h = 0.006234494161111027 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06728 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = -0.7998142259056535 y[1] (closed_form) = -0.6968399635021337 y[1] (numeric) = -0.6977662720051675 absolute error = 0.0009263085030337681 relative error = 0.1329298765212009 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0003501404672169057 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 35.12 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 32.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7000241927488283 y[1] (closed_form) = -0.764826601663965 y[1] (numeric) = -0.7752627175473598 absolute error = 0.01043611588339477 relative error = 1.364507440077247 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0003501404672169057 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3662 Order of pole (three term test) = 32.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5998840191247862 y[1] (closed_form) = -0.8254010970867516 y[1] (numeric) = -0.8746839604473265 absolute error = 0.04928286336057497 relative error = 5.970777544943731 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.0003501404672169057 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2152 Order of pole (three term test) = 32.95 NO COMPLEX POLE (six term test) for Equation 1 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ; 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 = 22.53 %