##############ECHO OF PROBLEM################# ##############temp/sing3postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=16; max_terms=20; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(-2.0); x_end=c(-0.7); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=c(0.001); glob_min_h=c(0.001); 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(2.0); 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)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -2 y[1] (closed_form) = 0.25 y[1] (numeric) = 0.25 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 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 7.641e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (closed_form) = 0.2770083102493075 y[1] (numeric) = 0.2770083099645017 absolute error = 2.848058455739988e-10 relative error = 1.028149102522136e-07 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 9 h = 0.05 Radius of convergence (given) for eq 1 = 1.9 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.9 Order of pole (three term test) = 8.747e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.8 y[1] (closed_form) = 0.308641975308642 y[1] (numeric) = 0.3086419745908527 absolute error = 7.177893279752823e-10 relative error = 2.325637422639914e-07 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 9 h = 0.05 Radius of convergence (given) for eq 1 = 1.8 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.7 y[1] (closed_form) = 0.3460207612456749 y[1] (numeric) = 0.3460207598541851 absolute error = 1.391489812263558e-09 relative error = 4.02140555744168e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.05 Radius of convergence (given) for eq 1 = 1.7 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.6 y[1] (closed_form) = 0.3906250000000002 y[1] (numeric) = 0.3906249975327418 absolute error = 2.467258342075951e-09 relative error = 6.316181355714431e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.05 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 3.229e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.5 y[1] (closed_form) = 0.4444444444444447 y[1] (numeric) = 0.4444444402085718 absolute error = 4.235872930191675e-09 relative error = 9.530714092931264e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.05 Radius of convergence (given) for eq 1 = 1.5 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.5 Order of pole (three term test) = 3.726e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.399999999999999 y[1] (closed_form) = 0.5102040816326534 y[1] (numeric) = 0.5102040743914148 absolute error = 7.241238608735046e-09 relative error = 1.419282767312068e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 Radius of convergence (given) for eq 1 = 1.4 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.4 Order of pole (three term test) = 7.524e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.299999999999999 y[1] (closed_form) = 0.5917159763313615 y[1] (numeric) = 0.5917159637866396 absolute error = 1.254472192790956e-08 relative error = 2.120058005816714e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 Radius of convergence (given) for eq 1 = 1.3 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.3 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.199999999999999 y[1] (closed_form) = 0.6944444444444453 y[1] (numeric) = 0.6944444221239814 absolute error = 2.232046392158793e-08 relative error = 3.214146804708658e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 Radius of convergence (given) for eq 1 = 1.2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.2 Order of pole (three term test) = 2.362e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.099999999999999 y[1] (closed_form) = 0.8264462809917367 y[1] (numeric) = 0.8264462397119765 absolute error = 4.127976016565782e-08 relative error = 4.994850980044589e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 Radius of convergence (given) for eq 1 = 1.1 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.1 Order of pole (three term test) = 2.778e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9999999999999991 y[1] (closed_form) = 1.000000000000002 y[1] (numeric) = 0.9999999196716317 absolute error = 8.03283700667734e-08 relative error = 8.032837006677327e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 2.547e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.899999999999999 y[1] (closed_form) = 1.23456790123457 y[1] (numeric) = 1.234567734459983 absolute error = 1.667745874733839e-07 relative error = 1.350874158534407e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.05 Radius of convergence (given) for eq 1 = 0.9 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9 Order of pole (three term test) = 3.455e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7999999999999989 y[1] (closed_form) = 1.562500000000004 y[1] (numeric) = 1.56249962417061 absolute error = 3.758293942723867e-07 relative error = 2.405308123343268e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.05 Radius of convergence (given) for eq 1 = 0.8 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8 Order of pole (three term test) = 3.229e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; Iterations = 26 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 103.8 %