##############ECHO OF PROBLEM################# ##############temp/sing7postode.ode################# diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=64; 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); /* 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) )/ ( c(x) - c(6.0) )/ ( 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) = -0.0009765625 y[1] (numeric) = -0.0009765625 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 5.914e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (closed_form) = -0.001108350100176561 y[1] (numeric) = -0.001108350099311493 absolute error = 8.650673493509897e-13 relative error = 7.805000867624625e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.05 Radius of convergence (given) for eq 1 = 3.9 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.9 Order of pole (three term test) = 2.377e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.199999999999999 y[1] (closed_form) = -0.001262065854394351 y[1] (numeric) = -0.001262065852383357 absolute error = 2.010993151516094e-12 relative error = 1.593413802072273e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.05 Radius of convergence (given) for eq 1 = 3.8 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.8 Order of pole (three term test) = 3.732e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.299999999999999 y[1] (closed_form) = -0.001442086727182296 y[1] (numeric) = -0.00144208672364209 absolute error = 3.54020545517697e-12 relative error = 2.454918548549576e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.05 Radius of convergence (given) for eq 1 = 3.7 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.7 Order of pole (three term test) = 5.716e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.399999999999999 y[1] (closed_form) = -0.001653817168792017 y[1] (numeric) = -0.001653817163195177 absolute error = 5.596839831867317e-12 relative error = 3.384195023175002e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.05 Radius of convergence (given) for eq 1 = 3.6 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.6 Order of pole (three term test) = 4.263e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.499999999999998 y[1] (closed_form) = -0.001903968584518351 y[1] (numeric) = -0.001903968576132751 absolute error = 8.38559950644413e-12 relative error = 4.404274090775214e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.05 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.5 Order of pole (three term test) = 6.185e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.599999999999998 y[1] (closed_form) = -0.002200925867886689 y[1] (numeric) = -0.002200925855686626 absolute error = 1.220006344213043e-11 relative error = 5.54315055320097e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.05 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.699999999999998 y[1] (closed_form) = -0.002555231782136432 y[1] (numeric) = -0.002555231764670798 absolute error = 1.746563354013131e-11 relative error = 6.835244325870225e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.05 Radius of convergence (given) for eq 1 = 3.3 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.3 Order of pole (three term test) = 2.975e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.799999999999997 y[1] (closed_form) = -0.002980232238769518 y[1] (numeric) = -0.00298023221396402 absolute error = 2.480549793348885e-11 relative error = 8.323343936353958e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.05 Radius of convergence (given) for eq 1 = 3.2 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.2 Order of pole (three term test) = 3.93e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.899999999999997 y[1] (closed_form) = -0.003492943259127715 y[1] (numeric) = -0.003492943223984484 absolute error = 3.514323077338788e-11 relative error = 1.006120860439174e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 Radius of convergence (given) for eq 1 = 3.1 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.1 Order of pole (three term test) = 5.013e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.999999999999996 y[1] (closed_form) = -0.004115226337448535 y[1] (numeric) = -0.004115226287583987 absolute error = 4.986454738703516e-11 relative error = 1.211708501504962e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 Radius of convergence (given) for eq 1 = 3 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( 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 %