##############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=20; ! /* 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=0.0001; /* # 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=1000000000; glob_max_minutes=30.0; 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 estimated_h = 1e-06 estimated_answer = 1 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 = 6.562503088236751e-96 estimated_step_error = 6.562503088236751e-96 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 = 4.300804047815587e-91 estimated_step_error = 4.300804047815587e-91 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 = 2.818577593557857e-86 estimated_step_error = 2.818577593557857e-86 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 = 1.84718648877761e-81 estimated_step_error = 1.84718648877761e-81 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 = 1.210576694767835e-76 estimated_step_error = 1.210576694767835e-76 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 = 7.93369516334265e-72 estimated_step_error = 7.93369516334265e-72 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 = 5.199504761864271e-67 estimated_step_error = 5.199504761864271e-67 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 = 3.407650074260886e-62 estimated_step_error = 3.407650074260886e-62 best_h = 0.0001 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 = 0.0001 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) = 3.591e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9899000000000011 y[1] (analytic) = -1.030922521337832 y[1] (numeric) = -1.030922521337836 absolute error = 3.552713678800501e-15 relative error = 3.446150030935525e-13 % Correct digits = 15 h = 0.0001 Radius of convergence (given) for eq 1 = 0.9899 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9899 Order of pole (three term test) = 2.595e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9799000000000022 y[1] (analytic) = -1.062807785163461 y[1] (numeric) = -1.062807785163469 absolute error = 7.549516567451064e-15 relative error = 7.103369652387275e-13 % Correct digits = 15 h = 0.0001 Radius of convergence (given) for eq 1 = 0.9799 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9799 Order of pole (three term test) = 7.501e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9699000000000033 y[1] (analytic) = -1.09602162234469 y[1] (numeric) = -1.096021622344703 absolute error = 1.265654248072678e-14 relative error = 1.154771240155917e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.9699 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9699 Order of pole (three term test) = 5.402e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9599000000000044 y[1] (analytic) = -1.130633957604819 y[1] (numeric) = -1.130633957604836 absolute error = 1.665334536937735e-14 relative error = 1.472921033139361e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.9599 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9599 Order of pole (three term test) = 3.877e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9499000000000055 y[1] (analytic) = -1.166719178850942 y[1] (numeric) = -1.166719178850962 absolute error = 1.998401444325282e-14 relative error = 1.71283842808981e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.9499 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9499 Order of pole (three term test) = 2.773e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9399000000000066 y[1] (analytic) = -1.204356473098711 y[1] (numeric) = -1.204356473098735 absolute error = 2.442490654175344e-14 relative error = 2.028046270960802e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.9399 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9399 Order of pole (three term test) = 7.906e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9299000000000077 y[1] (analytic) = -1.243630191606156 y[1] (numeric) = -1.243630191606184 absolute error = 2.886579864025407e-14 relative error = 2.321091819343315e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.9299 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9299 Order of pole (three term test) = 8.422e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9199000000000088 y[1] (analytic) = -1.284630247105139 y[1] (numeric) = -1.284630247105172 absolute error = 3.352873534367973e-14 relative error = 2.609991117618113e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.9199 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9199 Order of pole (three term test) = 3.972e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9099000000000099 y[1] (analytic) = -1.32745254633993 y[1] (numeric) = -1.327452546339968 absolute error = 3.796962744218035e-14 relative error = 2.860337836321962e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.9099 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9099 Order of pole (three term test) = 5.6e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.899900000000011 y[1] (analytic) = -1.372199461482977 y[1] (numeric) = -1.37219946148302 absolute error = 4.285460875053104e-14 relative error = 3.123059726624349e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.8999 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8999 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8899000000000121 y[1] (analytic) = -1.418980344403574 y[1] (numeric) = -1.418980344403622 absolute error = 4.773959005888173e-14 relative error = 3.364358798003479e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.8899 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8899 Order of pole (three term test) = 8.249e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8799000000000132 y[1] (analytic) = -1.467912088222083 y[1] (numeric) = -1.467912088222136 absolute error = 5.329070518200751e-14 relative error = 3.63037443519881e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.8799 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8799 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8699000000000143 y[1] (analytic) = -1.519119741097695 y[1] (numeric) = -1.519119741097753 absolute error = 5.795364188543317e-14 relative error = 3.814948902155445e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.8699 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8699 Order of pole (three term test) = 2.657e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8599000000000154 y[1] (analytic) = -1.572737177779795 y[1] (numeric) = -1.572737177779859 absolute error = 6.417089082333405e-14 relative error = 4.080204355181769e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.8599 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8599 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8499000000000165 y[1] (analytic) = -1.628907835111225 y[1] (numeric) = -1.628907835111294 absolute error = 6.905587213168474e-14 relative error = 4.23939713734445e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.8499 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8499 Order of pole (three term test) = 5.049e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8399000000000176 y[1] (analytic) = -1.687785518417234 y[1] (numeric) = -1.687785518417311 absolute error = 7.66053886991358e-14 relative error = 4.538810640523481e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.8399 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8399 Order of pole (three term test) = 3.457e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8299000000000187 y[1] (analytic) = -1.749535286559377 y[1] (numeric) = -1.74953528655946 absolute error = 8.37108160567368e-14 relative error = 4.784745795059777e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.8299 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8299 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8199000000000198 y[1] (analytic) = -1.814334424393878 y[1] (numeric) = -1.814334424393969 absolute error = 9.14823772291129e-14 relative error = 5.042200379330552e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.8199 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8199 Order of pole (three term test) = 6.396e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8099000000000209 y[1] (analytic) = -1.88237351246627 y[1] (numeric) = -1.882373512466369 absolute error = 9.903189379656396e-14 relative error = 5.261011862986385e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.8099 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8099 Order of pole (three term test) = 4.318e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.799900000000022 y[1] (analytic) = -1.953857605018461 y[1] (numeric) = -1.953857605018569 absolute error = 1.072475441787901e-13 relative error = 5.489015366489657e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.7999 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7999 Order of pole (three term test) = 5.804e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7899000000000231 y[1] (analytic) = -2.029007528804173 y[1] (numeric) = -2.029007528804289 absolute error = 1.159072837708663e-13 relative error = 5.712511270925548e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.7899 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7899 Order of pole (three term test) = 3.88e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7799000000000242 y[1] (analytic) = -2.108061316831302 y[1] (numeric) = -2.108061316831427 absolute error = 1.247890679678676e-13 relative error = 5.919612820154692e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.7799 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7799 Order of pole (three term test) = 2.581e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7699000000000253 y[1] (analytic) = -2.19127579300713 y[1] (numeric) = -2.191275793007266 absolute error = 1.363353874239692e-13 relative error = 6.221735660068309e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.7699 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7699 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7599000000000264 y[1] (analytic) = -2.278928325792075 y[1] (numeric) = -2.278928325792222 absolute error = 1.465494392505207e-13 relative error = 6.43062958987906e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.7599 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7599 Order of pole (three term test) = 4.496e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7499000000000275 y[1] (analytic) = -2.371318771413961 y[1] (numeric) = -2.371318771414118 absolute error = 1.567634910770721e-13 relative error = 6.61081474860496e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.7499 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7499 Order of pole (three term test) = 2.943e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7399000000000286 y[1] (analytic) = -2.468771630009576 y[1] (numeric) = -2.468771630009744 absolute error = 1.678657213233237e-13 relative error = 6.799564580328255e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.7399 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7399 Order of pole (three term test) = 7.66e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7299000000000297 y[1] (analytic) = -2.571638441305081 y[1] (numeric) = -2.571638441305262 absolute error = 1.807443084089755e-13 relative error = 7.028371698987728e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.7299 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7299 Order of pole (three term test) = 2.478e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7199000000000308 y[1] (analytic) = -2.680300450194177 y[1] (numeric) = -2.680300450194368 absolute error = 1.91402449445377e-13 relative error = 7.141081867576102e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.7199 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7199 Order of pole (three term test) = 3.187e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7099000000000319 y[1] (analytic) = -2.795171576909012 y[1] (numeric) = -2.795171576909214 absolute error = 2.020605904817785e-13 relative error = 7.228915468052354e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.7099 Order of pole (given) = 4 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7099 Order of pole (three term test) = 4.074e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ; Iterations = 3001 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 30 Minutes 0.0 Seconds Percent Done = 100.1 %