##############ECHO OF PROBLEM################# ##############temp/sing5_backpostode.ode################# diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=20; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(-0.7); x_end=c(-1.0); 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(0.0); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(4.0); 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(x)/c(x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -0.7 y[1] (closed_form) = -2.915451895043732 y[1] (numeric) = -2.915451895043732 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 = 0.7 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 2.408e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6499999999999999 y[1] (closed_form) = -3.64132908511607 y[1] (numeric) = -3.641324368993549 absolute error = 4.716122520065369e-06 relative error = 0.0001295165147072951 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 6 h = 0.05 Radius of convergence (given) for eq 1 = 0.65 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.65 Order of pole (three term test) = 7.192e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5999999999999999 y[1] (closed_form) = -4.629629629629632 y[1] (numeric) = -4.629615614915013 absolute error = 1.401471461992543e-05 relative error = 0.0003027178357903891 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 6 h = 0.05 Radius of convergence (given) for eq 1 = 0.6 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6 Order of pole (three term test) = 4.442e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5499999999999998 y[1] (closed_form) = -6.010518407212628 y[1] (numeric) = -6.01048501273744 absolute error = 3.33944751886861e-05 relative error = 0.0005556005809517644 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.05 Radius of convergence (given) for eq 1 = 0.55 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.55 Order of pole (three term test) = 4.39e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4999999999999998 y[1] (closed_form) = -8.000000000000011 y[1] (numeric) = -7.99992348549991 absolute error = 7.651450010115468e-05 relative error = 0.0009564312512644322 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.05 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 6.653e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4499999999999998 y[1] (closed_form) = -10.97393689986284 y[1] (numeric) = -10.97375663807401 absolute error = 0.0001802617888309044 relative error = 0.001642635550721614 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.05 SETTING H FOR POLE Radius of convergence (given) for eq 1 = 0.45 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.45 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4949999999999998 y[1] (closed_form) = -8.244881217026924 y[1] (numeric) = -8.244605697562505 absolute error = 0.0002755194644183945 relative error = 0.003341703260071294 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = -0.04500000000000001 Radius of convergence (given) for eq 1 = 0.495 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.495 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5399999999999998 y[1] (closed_form) = -6.350657928161365 y[1] (numeric) = -6.350341336084187 absolute error = 0.000316592077177269 relative error = 0.004985185484064143 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = -0.04500000000000001 Radius of convergence (given) for eq 1 = 0.54 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.54 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5849999999999999 y[1] (closed_form) = -4.994964451462373 y[1] (numeric) = -4.994628827081359 absolute error = 0.0003356243810133108 relative error = 0.006719254646848393 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 5 h = -0.04500000000000001 Radius of convergence (given) for eq 1 = 0.585 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.585 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6299999999999999 y[1] (closed_form) = -3.999248141349428 y[1] (numeric) = -3.998903146227006 absolute error = 0.0003449951224223646 relative error = 0.008626499537634497 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 5 h = -0.04500000000000001 Radius of convergence (given) for eq 1 = 0.63 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.63 Order of pole (three term test) = 5.118e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6749999999999999 y[1] (closed_form) = -3.251536859218616 y[1] (numeric) = -3.251187005128261 absolute error = 0.0003498540903548175 relative error = 0.01075965321945917 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 4 h = -0.04500000000000001 Radius of convergence (given) for eq 1 = 0.675 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.675 Order of pole (three term test) = 5.819e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.72 y[1] (closed_form) = -2.679183813443073 y[1] (numeric) = -2.678831324627672 absolute error = 0.000352488815400509 relative error = 0.01315657453706092 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 4 h = -0.04500000000000001 Radius of convergence (given) for eq 1 = 0.72 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.72 Order of pole (three term test) = 2.869e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.765 y[1] (closed_form) = -2.23365294114855 y[1] (numeric) = -2.233298966845148 absolute error = 0.000353974303402449 relative error = 0.01584732779571541 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 4 h = -0.04500000000000001 Radius of convergence (given) for eq 1 = 0.765 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.765 Order of pole (three term test) = 2.495e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8100000000000001 y[1] (closed_form) = -1.88167642315892 y[1] (numeric) = -1.881321582066535 absolute error = 0.0003548410923854828 relative error = 0.01885771049784334 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 4 h = -0.04500000000000001 Radius of convergence (given) for eq 1 = 0.81 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.81 Order of pole (three term test) = 3.885e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8550000000000001 y[1] (closed_form) = -1.599932482849223 y[1] (numeric) = -1.599577120344845 absolute error = 0.000355362504377954 relative error = 0.02221109379222743 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 4 h = -0.04500000000000001 Radius of convergence (given) for eq 1 = 0.855 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.855 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9000000000000001 y[1] (closed_form) = -1.371742112482853 y[1] (numeric) = -1.371386427681508 absolute error = 0.0003556848013441805 relative error = 0.02592942201799077 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 4 h = -0.04500000000000001 Radius of convergence (given) for eq 1 = 0.9 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9 Order of pole (three term test) = 7.072e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9450000000000002 y[1] (closed_form) = -1.184962412251681 y[1] (numeric) = -1.184606523305157 absolute error = 0.0003558889465242743 relative error = 0.0300337751513999 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 4 h = -0.04500000000000001 Radius of convergence (given) for eq 1 = 0.945 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.945 Order of pole (three term test) = 8.424e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9900000000000002 y[1] (closed_form) = -1.030610152128364 y[1] (numeric) = -1.030254130990184 absolute error = 0.0003560211381798961 relative error = 0.03454469543548151 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 4 h = -0.04500000000000001 Radius of convergence (given) for eq 1 = 0.99 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.99 Order of pole (three term test) = 4.666e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ; Iterations = 18 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 = 0 %