##############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=(5.0); glob_subiter_method=3; glob_max_iter=1000; glob_upper_ratio_limit=c(1.1); glob_lower_ratio_limit=c(0.9); /* 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 Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 8 estimated_h = 0.001 estimated_answer = 1 desired_abs_gbl_error = 1e-08 range = 1.3 estimated_steps = 1300 step_error = 1.386750490563073e-11 est_needed_step_err = 1.386750490563073e-11 opt_iter = 1 SETTING H FOR MIN H SETTING H FOR DISPLAY INTERVAL 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 Radius of convergence (ratio test) for eq 1 = 2.143 Order of pole (ratio test) = 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] = -1.95 y[1] (closed_form) = 0.2629848783694938 y[1] (numeric) = 0.2629848782415491 absolute error = 1.279447103819109e-10 relative error = 4.865097612272162e-08 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 10 h = 0.05 Radius of convergence (given) for eq 1 = 1.95 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 2.089 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.95 Order of pole (three term test) = 0 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 Radius of convergence (ratio test) for eq 1 = 2.036 Order of pole (ratio test) = 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] = -1.85 y[1] (closed_form) = 0.2921840759678598 y[1] (numeric) = 0.2921840754897139 absolute error = 4.781458562419516e-10 relative error = 1.636454192988079e-07 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 9 h = 0.05 Radius of convergence (given) for eq 1 = 1.85 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.982 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.85 Order of pole (three term test) = 3.93e-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 Radius of convergence (ratio test) for eq 1 = 1.929 Order of pole (ratio test) = 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] = -1.75 y[1] (closed_form) = 0.326530612244898 y[1] (numeric) = 0.3265306112283081 absolute error = 1.016589978863891e-09 relative error = 3.113306810270665e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.05 Radius of convergence (given) for eq 1 = 1.75 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.875 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.75 Order of pole (three term test) = 8.903e-14 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 Radius of convergence (ratio test) for eq 1 = 1.821 Order of pole (ratio test) = 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] = -1.65 y[1] (closed_form) = 0.3673094582185493 y[1] (numeric) = 0.3673094563535533 absolute error = 1.864995935463298e-09 relative error = 5.077451434298828e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.05 Radius of convergence (given) for eq 1 = 1.65 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.768 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.65 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 Radius of convergence (ratio test) for eq 1 = 1.714 Order of pole (ratio test) = 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] = -1.55 y[1] (closed_form) = 0.4162330905306974 y[1] (numeric) = 0.4162330872916747 absolute error = 3.23902271670562e-09 relative error = 7.781752076885247e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.05 Radius of convergence (given) for eq 1 = 1.55 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.661 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.55 Order of pole (three term test) = 0 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 Radius of convergence (ratio test) for eq 1 = 1.607 Order of pole (ratio test) = 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] = -1.45 y[1] (closed_form) = 0.475624256837099 y[1] (numeric) = 0.4756242513027045 absolute error = 5.534394553752264e-09 relative error = 1.163606454926413e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 Radius of convergence (given) for eq 1 = 1.45 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.554 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.45 Order of pole (three term test) = 0 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 Radius of convergence (ratio test) for eq 1 = 1.5 Order of pole (ratio test) = 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] = -1.349999999999999 y[1] (closed_form) = 0.5486968449931418 y[1] (numeric) = 0.5486968354865188 absolute error = 9.506622933308506e-09 relative error = 1.732582029595474e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 Radius of convergence (given) for eq 1 = 1.35 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.446 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.35 Order of pole (three term test) = 0 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 Radius of convergence (ratio test) for eq 1 = 1.393 Order of pole (ratio test) = 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] = -1.249999999999999 y[1] (closed_form) = 0.6400000000000007 y[1] (numeric) = 0.6399999833350828 absolute error = 1.666491789009683e-08 relative error = 2.603893420327627e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 Radius of convergence (given) for eq 1 = 1.25 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.339 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.25 Order of pole (three term test) = 4.018e-14 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 Radius of convergence (ratio test) for eq 1 = 1.286 Order of pole (ratio test) = 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] = -1.149999999999999 y[1] (closed_form) = 0.7561436672967874 y[1] (numeric) = 0.7561436371112209 absolute error = 3.018556649081461e-08 relative error = 3.992041168410227e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 Radius of convergence (given) for eq 1 = 1.15 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.232 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.15 Order of pole (three term test) = 2.635e-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 Radius of convergence (ratio test) for eq 1 = 1.179 Order of pole (ratio test) = 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] = -1.049999999999999 y[1] (closed_form) = 0.9070294784580513 y[1] (numeric) = 0.907029421285402 absolute error = 5.717264928151167e-08 relative error = 6.303284583286652e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 Radius of convergence (given) for eq 1 = 1.05 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.125 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.05 Order of pole (three term test) = 2.752e-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 Radius of convergence (ratio test) for eq 1 = 1.071 Order of pole (ratio test) = 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] = -0.9499999999999991 y[1] (closed_form) = 1.108033240997232 y[1] (numeric) = 1.108033126298148 absolute error = 1.146990842304518e-07 relative error = 1.035159235179826e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.05 Radius of convergence (given) for eq 1 = 0.95 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.018 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.95 Order of pole (three term test) = 4.373e-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 Radius of convergence (ratio test) for eq 1 = 0.9643 Order of pole (ratio test) = 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] = -0.849999999999999 y[1] (closed_form) = 1.384083044982702 y[1] (numeric) = 1.38408279748995 absolute error = 2.474927520701442e-07 relative error = 1.788135133706788e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.05 Radius of convergence (given) for eq 1 = 0.85 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.9107 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.85 Order of pole (three term test) = 4.975e-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 Radius of convergence (ratio test) for eq 1 = 0.8571 Order of pole (ratio test) = 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 TOP MAIN SOLVE Loop x[1] = -0.7499999999999989 y[1] (closed_form) = 1.777777777777783 y[1] (numeric) = 1.777777191990109 absolute error = 5.857876739234769e-07 relative error = 3.295055665819548e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.05 Radius of convergence (given) for eq 1 = 0.75 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.8036 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.75 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 / x / x ; Iterations = 26 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 5 Minutes 0.0 Seconds Percent Done = 103.8 %