##############ECHO OF PROBLEM################# ##############temp/sing6postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=30; max_terms=20; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(2.0); x_end=c(3.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=1; array_given_rad_poles[1][1]=c(6.0); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(3.0); array_given_ord_poles[1][2]=c(0.0); /* 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)/ ( c(x) - c(6.0) ) / ( c(x) - c(6.0) )); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 2 y[1] (closed_form) = 0.0625 y[1] (numeric) = 0.0625 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 7.641e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (closed_form) = 0.06574621959237342 y[1] (numeric) = 0.06574621959134538 absolute error = 1.028038765227279e-12 relative error = 1.563646961910692e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 3.9 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.9 Order of pole (three term test) = 7.15e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.199999999999999 y[1] (closed_form) = 0.06925207756232683 y[1] (numeric) = 0.06925207756003747 absolute error = 2.28936314350392e-12 relative error = 3.305840379219662e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 3.8 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.8 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.299999999999999 y[1] (closed_form) = 0.07304601899196489 y[1] (numeric) = 0.07304601898811962 absolute error = 3.845271323577037e-12 relative error = 5.264176441976968e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 3.7 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.7 Order of pole (three term test) = 3.93e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.399999999999999 y[1] (closed_form) = 0.07716049382716043 y[1] (numeric) = 0.07716049382138501 absolute error = 5.775421807463488e-12 relative error = 7.484946662472687e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 3.6 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.6 Order of pole (three term test) = 6.91e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.499999999999998 y[1] (closed_form) = 0.08163265306122441 y[1] (numeric) = 0.08163265305304021 absolute error = 8.184203315053651e-12 relative error = 1.002564906094073e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.05 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.5 Order of pole (three term test) = 2.968e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.599999999999998 y[1] (closed_form) = 0.08650519031141858 y[1] (numeric) = 0.08650519030020927 absolute error = 1.120931125697666e-11 relative error = 1.295796381306504e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.05 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.4 Order of pole (three term test) = 7.463e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.699999999999998 y[1] (closed_form) = 0.09182736455463715 y[1] (numeric) = 0.09182736453960323 absolute error = 1.503391855450786e-11 relative error = 1.637193730585909e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.05 Radius of convergence (given) for eq 1 = 3.3 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.3 Order of pole (three term test) = 4.064e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.799999999999997 y[1] (closed_form) = 0.09765624999999983 y[1] (numeric) = 0.09765624998009613 absolute error = 1.9903703685209e-11 relative error = 2.038139257365405e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.05 Radius of convergence (given) for eq 1 = 3.2 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.2 Order of pole (three term test) = 9.686e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.899999999999997 y[1] (closed_form) = 0.1040582726326741 y[1] (numeric) = 0.1040582726065229 absolute error = 2.615115068937968e-11 relative error = 2.513125581249392e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.05 Radius of convergence (given) for eq 1 = 3.1 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.1 Order of pole (three term test) = 2.491e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.999999999999996 y[1] (closed_form) = 0.1111111111111108 y[1] (numeric) = 0.1111111110768803 absolute error = 3.42305211953331e-11 relative error = 3.080746907579986e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.05 Radius of convergence (given) for eq 1 = 3 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3 Order of pole (three term test) = 3.726e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; Iterations = 21 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 110 %