##############ECHO OF PROBLEM################# ##############temp/sing5postode.ode################# diff ( y , x , 1 ) = neg ( 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(-1.0); 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(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=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=true; glob_h=c(0.001); glob_display_interval=c(0.01); // 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] = -1 y[1] (closed_form) = -1 y[1] (numeric) = -1 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 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] = -0.99 y[1] (closed_form) = -1.030610152128365 y[1] (numeric) = -1.030610152128364 absolute error = 4.440892098500626e-16 relative error = 4.308993162283058e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 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) = 4.029e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.98 y[1] (closed_form) = -1.062482469039261 y[1] (numeric) = -1.06248246903926 absolute error = 8.881784197001252e-16 relative error = 8.359464231944002e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.98 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.98 Order of pole (three term test) = 2.911e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.97 y[1] (closed_form) = -1.095682681529968 y[1] (numeric) = -1.095682681529967 absolute error = 6.661338147750939e-16 relative error = 6.079623471322293e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.97 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.97 Order of pole (three term test) = 4.193e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.96 y[1] (closed_form) = -1.130280671296297 y[1] (numeric) = -1.130280671296295 absolute error = 1.110223024625157e-15 relative error = 9.822542779147624e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.96 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.96 Order of pole (three term test) = 3.01e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.95 y[1] (closed_form) = -1.166350779997084 y[1] (numeric) = -1.166350779997083 absolute error = 8.881784197001252e-16 relative error = 7.615019725903948e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.95 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.95 Order of pole (three term test) = 8.612e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9399999999999999 y[1] (closed_form) = -1.203972144900456 y[1] (numeric) = -1.203972144900455 absolute error = 8.881784197001252e-16 relative error = 7.377067845482087e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.94 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.94 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9299999999999999 y[1] (closed_form) = -1.24322906371176 y[1] (numeric) = -1.243229063711759 absolute error = 1.332267629550188e-15 relative error = 1.0716187937021e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.93 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.93 Order of pole (three term test) = 8.718e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9199999999999999 y[1] (closed_form) = -1.284211391468727 y[1] (numeric) = -1.284211391468725 absolute error = 1.77635683940025e-15 relative error = 1.383227754558902e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.92 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.92 Order of pole (three term test) = 6.168e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9099999999999999 y[1] (closed_form) = -1.327014972709937 y[1] (numeric) = -1.327014972709935 absolute error = 1.998401444325282e-15 relative error = 1.505937374801647e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.91 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.91 Order of pole (three term test) = 4.348e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8999999999999999 y[1] (closed_form) = -1.371742112482853 y[1] (numeric) = -1.371742112482851 absolute error = 2.664535259100376e-15 relative error = 1.942446203884174e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 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) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8899999999999999 y[1] (closed_form) = -1.41850209016283 y[1] (numeric) = -1.418502090162827 absolute error = 3.108624468950438e-15 relative error = 2.191483883251521e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.89 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.89 Order of pole (three term test) = 8.541e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8799999999999999 y[1] (closed_form) = -1.467411720510895 y[1] (numeric) = -1.467411720510891 absolute error = 3.552713678800501e-15 relative error = 2.421074896119534e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.88 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.88 Order of pole (three term test) = 2.975e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8699999999999999 y[1] (closed_form) = -1.518595966912831 y[1] (numeric) = -1.518595966912827 absolute error = 3.996802888650564e-15 relative error = 2.631906692585061e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.87 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.87 Order of pole (three term test) = 4.127e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8599999999999999 y[1] (closed_form) = -1.572188612323444 y[1] (numeric) = -1.572188612323439 absolute error = 4.440892098500626e-15 relative error = 2.824656064603913e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.86 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.86 Order of pole (three term test) = 5.702e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8499999999999999 y[1] (closed_form) = -1.628332994097294 y[1] (numeric) = -1.628332994097289 absolute error = 5.10702591327572e-15 relative error = 3.13635228899045e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.85 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.85 Order of pole (three term test) = 7.843e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8399999999999999 y[1] (closed_form) = -1.68718280963179 y[1] (numeric) = -1.687182809631784 absolute error = 5.551115123125783e-15 relative error = 3.290168137937142e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.84 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.84 Order of pole (three term test) = 5.37e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8299999999999998 y[1] (closed_form) = -1.748903000592879 y[1] (numeric) = -1.748903000592873 absolute error = 6.439293542825908e-15 relative error = 3.681904336971795e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.83 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.83 Order of pole (three term test) = 3.661e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8199999999999998 y[1] (closed_form) = -1.813670724452635 y[1] (numeric) = -1.813670724452628 absolute error = 6.661338147750939e-15 relative error = 3.672848691849138e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.82 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.82 Order of pole (three term test) = 2.484e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8099999999999998 y[1] (closed_form) = -1.881676423158922 y[1] (numeric) = -1.881676423158914 absolute error = 7.105427357601002e-15 relative error = 3.776115420350832e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 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) = 6.709e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7999999999999998 y[1] (closed_form) = -1.953125000000001 y[1] (numeric) = -1.953124999999993 absolute error = 7.993605777301127e-15 relative error = 4.092726157978174e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.8 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7899999999999998 y[1] (closed_form) = -2.028237117144893 y[1] (numeric) = -2.028237117144884 absolute error = 8.881784197001252e-15 relative error = 4.379065998705297e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.79 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.79 Order of pole (three term test) = 3.014e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7799999999999998 y[1] (closed_form) = -2.107250627960689 y[1] (numeric) = -2.107250627960679 absolute error = 1.021405182655144e-14 relative error = 4.847098722393636e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.78 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.78 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7699999999999998 y[1] (closed_form) = -2.190422160062911 y[1] (numeric) = -2.190422160062899 absolute error = 1.199040866595169e-14 relative error = 5.474017239492919e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.77 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.77 Order of pole (three term test) = 2.654e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7599999999999998 y[1] (closed_form) = -2.278028867181807 y[1] (numeric) = -2.278028867181794 absolute error = 1.243449787580175e-14 relative error = 5.458446139527946e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.76 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.76 Order of pole (three term test) = 3.493e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7499999999999998 y[1] (closed_form) = -2.370370370370372 y[1] (numeric) = -2.370370370370359 absolute error = 1.332267629550188e-14 relative error = 5.62050406216485e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.75 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.75 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7399999999999998 y[1] (closed_form) = -2.46777091189071 y[1] (numeric) = -2.467770911890695 absolute error = 1.509903313490213e-14 relative error = 6.118490603057574e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.74 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.74 Order of pole (three term test) = 5.952e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7299999999999998 y[1] (closed_form) = -2.570581748355473 y[1] (numeric) = -2.570581748355456 absolute error = 1.687538997430238e-14 relative error = 6.564813581633183e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.73 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.73 Order of pole (three term test) = 7.702e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7199999999999998 y[1] (closed_form) = -2.679183813443075 y[1] (numeric) = -2.679183813443057 absolute error = 1.820765760385257e-14 relative error = 6.795971785322756e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 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) = 2.477e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7099999999999997 y[1] (closed_form) = -2.79399068483506 y[1] (numeric) = -2.793990684835039 absolute error = 2.131628207280301e-14 relative error = 7.629331832958987e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.71 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.71 Order of pole (three term test) = 3.166e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = neg ( 3.0 ) / x / x / x / x ; Iterations = 300 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.3 %