##############ECHO OF PROBLEM################# ##############temp/sing5postode.ode################# diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-1.0; x_end=-0.7; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=100; glob_max_h=0.001; /* # Not Given = 0 */ /* # No Pole = 3 */ /* # Pole = 4 */ glob_type_given_pole=4; /* # Real Part */ array_given_rad_poles[1][1]=0.0; /* # Imag Part */ array_given_rad_poles[1][2]=0.0; /* # Order */ array_given_ord_poles[1][1]=4.0; /* # Not Used */ array_given_ord_poles[1][2]=0.0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=10000000; glob_max_minutes=3; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(1.0/x/x/x); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 0.3 estimated_steps = 300000.0000000001 step_error = 3.333333333333333e-16 est_needed_step_err = 3.333333333333333e-16 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.916668085586272e-216 estimated_step_error = 2.916668085586272e-216 best_h = 2e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.004320021615875e-205 estimated_step_error = 2.004320021615875e-205 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.377359571104255e-194 estimated_step_error = 1.377359571104255e-194 best_h = 8e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.465161319088796e-184 estimated_step_error = 9.465161319088796e-184 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.504434645351289e-173 estimated_step_error = 6.504434645351289e-173 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.469848245524189e-162 estimated_step_error = 4.469848245524189e-162 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.071704144925311e-151 estimated_step_error = 3.071704144925311e-151 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.110924741248204e-140 estimated_step_error = 2.110924741248204e-140 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.450706778015151e-129 estimated_step_error = 1.450706778015151e-129 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.97042294498812e-119 estimated_step_error = 9.97042294498812e-119 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.853329936478012e-108 estimated_step_error = 6.853329936478012e-108 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] = -1 y[1] (analytic) = -1 y[1] (numeric) = -1 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 1.031 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9992 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.99 y[1] (analytic) = -1.030610152128365 y[1] (numeric) = -1.030610152128364 absolute error = 2.220446049250313e-16 relative error = 2.154496581141529e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.99 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 1.021 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9893 Order of pole (three term test) = 1225 Radius of convergence (six term test) for eq 1 = 1.051 Order of pole (six term test) = -7.375e-11 TOP MAIN SOLVE Loop x[1] = -0.98 y[1] (analytic) = -1.062482469039261 y[1] (numeric) = -1.06248246903926 absolute error = 8.881784197001252e-16 relative error = 8.359464231944002e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.98 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 1.011 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9793 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.97 y[1] (analytic) = -1.095682681529968 y[1] (numeric) = -1.095682681529967 absolute error = 6.661338147750939e-16 relative error = 6.079623471322293e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.97 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 1 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9693 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.96 y[1] (analytic) = -1.130280671296297 y[1] (numeric) = -1.130280671296295 absolute error = 1.110223024625157e-15 relative error = 9.822542779147624e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.96 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.99 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9593 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.95 y[1] (analytic) = -1.166350779997084 y[1] (numeric) = -1.166350779997083 absolute error = 8.881784197001252e-16 relative error = 7.615019725903948e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.95 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.9797 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9493 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9399999999999999 y[1] (analytic) = -1.203972144900456 y[1] (numeric) = -1.203972144900455 absolute error = 1.110223024625157e-15 relative error = 9.221334806852608e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.94 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.9694 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9393 Order of pole (three term test) = 1225 Radius of convergence (six term test) for eq 1 = 3.693 Order of pole (six term test) = -4.612e-10 TOP MAIN SOLVE Loop x[1] = -0.9299999999999999 y[1] (analytic) = -1.24322906371176 y[1] (numeric) = -1.243229063711759 absolute error = 1.110223024625157e-15 relative error = 8.930156614184169e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.93 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.9591 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9293 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9199999999999999 y[1] (analytic) = -1.284211391468727 y[1] (numeric) = -1.284211391468725 absolute error = 1.77635683940025e-15 relative error = 1.383227754558902e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.92 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.9487 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9193 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9099999999999999 y[1] (analytic) = -1.327014972709937 y[1] (numeric) = -1.327014972709935 absolute error = 1.998401444325282e-15 relative error = 1.505937374801647e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.91 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.9384 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9093 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8999999999999999 y[1] (analytic) = -1.371742112482854 y[1] (numeric) = -1.371742112482851 absolute error = 2.886579864025407e-15 relative error = 2.104316720874521e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.9 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.9281 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8993 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8899999999999999 y[1] (analytic) = -1.41850209016283 y[1] (numeric) = -1.418502090162827 absolute error = 3.108624468950438e-15 relative error = 2.191483883251521e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.89 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.9178 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8893 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8799999999999999 y[1] (analytic) = -1.467411720510895 y[1] (numeric) = -1.467411720510891 absolute error = 3.552713678800501e-15 relative error = 2.421074896119534e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.88 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.9075 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8793 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8699999999999999 y[1] (analytic) = -1.518595966912832 y[1] (numeric) = -1.518595966912827 absolute error = 4.218847493575595e-15 relative error = 2.778123731062009e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.87 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.8972 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8693 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8599999999999999 y[1] (analytic) = -1.572188612323444 y[1] (numeric) = -1.572188612323439 absolute error = 4.440892098500626e-15 relative error = 2.824656064603913e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.86 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.8869 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8594 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8499999999999999 y[1] (analytic) = -1.628332994097294 y[1] (numeric) = -1.628332994097289 absolute error = 5.10702591327572e-15 relative error = 3.13635228899045e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.85 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.8766 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8494 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8399999999999999 y[1] (analytic) = -1.68718280963179 y[1] (numeric) = -1.687182809631784 absolute error = 5.551115123125783e-15 relative error = 3.290168137937142e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.84 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.8662 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8394 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8299999999999998 y[1] (analytic) = -1.748903000592879 y[1] (numeric) = -1.748903000592873 absolute error = 6.439293542825908e-15 relative error = 3.681904336971795e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.83 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.8559 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8294 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8199999999999998 y[1] (analytic) = -1.813670724452635 y[1] (numeric) = -1.813670724452628 absolute error = 6.883382752675971e-15 relative error = 3.795276981577442e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.82 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.8456 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8194 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8099999999999998 y[1] (analytic) = -1.881676423158922 y[1] (numeric) = -1.881676423158914 absolute error = 7.549516567451064e-15 relative error = 4.012122634122759e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.81 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.8353 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8094 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7999999999999998 y[1] (analytic) = -1.953125000000001 y[1] (numeric) = -1.953124999999993 absolute error = 7.993605777301127e-15 relative error = 4.092726157978174e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.8 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.825 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7994 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7899999999999998 y[1] (analytic) = -2.028237117144893 y[1] (numeric) = -2.028237117144884 absolute error = 8.881784197001252e-15 relative error = 4.379065998705297e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.79 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.8147 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7894 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7799999999999998 y[1] (analytic) = -2.107250627960689 y[1] (numeric) = -2.107250627960679 absolute error = 1.021405182655144e-14 relative error = 4.847098722393636e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.78 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.8044 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7794 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7699999999999998 y[1] (analytic) = -2.190422160062911 y[1] (numeric) = -2.190422160062899 absolute error = 1.199040866595169e-14 relative error = 5.474017239492919e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.77 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.7941 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7694 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7599999999999998 y[1] (analytic) = -2.278028867181807 y[1] (numeric) = -2.278028867181794 absolute error = 1.243449787580175e-14 relative error = 5.458446139527946e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.76 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.7837 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7594 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7499999999999998 y[1] (analytic) = -2.370370370370372 y[1] (numeric) = -2.370370370370359 absolute error = 1.332267629550188e-14 relative error = 5.62050406216485e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.75 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.7734 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7494 Order of pole (three term test) = 1225 Radius of convergence (six term test) for eq 1 = 0.6808 Order of pole (six term test) = 1.032e-10 TOP MAIN SOLVE Loop x[1] = -0.7399999999999998 y[1] (analytic) = -2.46777091189071 y[1] (numeric) = -2.467770911890695 absolute error = 1.509903313490213e-14 relative error = 6.118490603057574e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.74 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.7631 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7394 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7299999999999998 y[1] (analytic) = -2.570581748355473 y[1] (numeric) = -2.570581748355456 absolute error = 1.687538997430238e-14 relative error = 6.564813581633183e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.73 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.7528 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7295 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7199999999999998 y[1] (analytic) = -2.679183813443076 y[1] (numeric) = -2.679183813443057 absolute error = 1.865174681370263e-14 relative error = 6.961727194720872e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.72 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.7425 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7195 Order of pole (three term test) = 1225 Radius of convergence (six term test) for eq 1 = 2.394 Order of pole (six term test) = 2.66e-10 TOP MAIN SOLVE Loop x[1] = -0.7099999999999997 y[1] (analytic) = -2.79399068483506 y[1] (numeric) = -2.793990684835039 absolute error = 2.087219286295294e-14 relative error = 7.470387419772343e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.71 Order of pole (given) = 4 Radius of convergence (ratio test) for eq 1 = 0.7322 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7095 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ; Iterations = 300 Total Elapsed Time = 0 Seconds Elapsed Time(since restart) = 0 Seconds Time to Timeout = 3 Minutes 0 Seconds Percent Done = 100.3 %