##############ECHO OF PROBLEM################# ##############temp/sing3postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 / 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]=3.0; // # 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); } // 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 = 8.333337387389347e-217 estimated_step_error = 8.333337387389347e-217 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 = 5.726628633188214e-206 estimated_step_error = 5.726628633188214e-206 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 = 3.935313060297871e-195 estimated_step_error = 3.935313060297871e-195 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 = 2.704331805453941e-184 estimated_step_error = 2.704331805453941e-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 = 1.858409898671796e-173 estimated_step_error = 1.858409898671796e-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 = 1.277099498721197e-162 estimated_step_error = 1.277099498721197e-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 = 8.776297556929459e-152 estimated_step_error = 8.776297556929459e-152 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 = 6.031213546423438e-141 estimated_step_error = 6.031213546423438e-141 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 = 4.144876508614716e-130 estimated_step_error = 4.144876508614716e-130 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 = 2.848692269996605e-119 estimated_step_error = 2.848692269996605e-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 = 1.958094267565146e-108 estimated_step_error = 1.958094267565146e-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) = 3 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) = 1.020304050607081 y[1] (numeric) = 1.020304050607081 absolute error = 2.220446049250313e-16 relative error = 2.176259172870232e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.99 Order of pole (given) = 3 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.98 y[1] (analytic) = 1.041232819658476 y[1] (numeric) = 1.041232819658476 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.98 Order of pole (given) = 3 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) = 1.062812201084069 y[1] (numeric) = 1.062812201084068 absolute error = 2.220446049250313e-16 relative error = 2.089217687739619e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.97 Order of pole (given) = 3 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) = 1.085069444444444 y[1] (numeric) = 1.085069444444444 absolute error = 2.220446049250313e-16 relative error = 2.046363078989088e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.96 Order of pole (given) = 3 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) = 1.10803324099723 y[1] (numeric) = 1.10803324099723 absolute error = 4.440892098500626e-16 relative error = 4.007905118896815e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.95 Order of pole (given) = 3 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) = 1.131733816206428 y[1] (numeric) = 1.131733816206428 absolute error = 4.440892098500626e-16 relative error = 3.923972258235153e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.94 Order of pole (given) = 3 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9299999999999999 y[1] (analytic) = 1.156203029251937 y[1] (numeric) = 1.156203029251936 absolute error = 4.440892098500626e-16 relative error = 3.840927575993191e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.93 Order of pole (given) = 3 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) = 1.181474480151229 y[1] (numeric) = 1.181474480151228 absolute error = 6.661338147750939e-16 relative error = 5.638156608256394e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.92 Order of pole (given) = 3 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 Radius of convergence (six term test) for eq 1 = 0.662 Order of pole (six term test) = -4.064e-11 TOP MAIN SOLVE Loop x[1] = -0.9099999999999999 y[1] (analytic) = 1.207583625166043 y[1] (numeric) = 1.207583625166042 absolute error = 6.661338147750939e-16 relative error = 5.516254120152552e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.91 Order of pole (given) = 3 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) = 1.234567901234568 y[1] (numeric) = 1.234567901234567 absolute error = 6.661338147750939e-16 relative error = 5.39568389967826e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.9 Order of pole (given) = 3 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) = 1.262466860244919 y[1] (numeric) = 1.262466860244918 absolute error = 8.881784197001252e-16 relative error = 7.03526126244469e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.89 Order of pole (given) = 3 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) = 1.291322314049587 y[1] (numeric) = 1.291322314049586 absolute error = 6.661338147750939e-16 relative error = 5.158540261618326e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.88 Order of pole (given) = 3 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) = 1.321178491214163 y[1] (numeric) = 1.321178491214163 absolute error = 6.661338147750939e-16 relative error = 5.041966844032685e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.87 Order of pole (given) = 3 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) = 1.352082206598161 y[1] (numeric) = 1.352082206598161 absolute error = 6.661338147750939e-16 relative error = 4.926725694076593e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.86 Order of pole (given) = 3 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) = 1.384083044982699 y[1] (numeric) = 1.384083044982698 absolute error = 8.881784197001252e-16 relative error = 6.417089082333404e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.85 Order of pole (given) = 3 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) = 1.417233560090703 y[1] (numeric) = 1.417233560090702 absolute error = 8.881784197001252e-16 relative error = 6.266986929404081e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.84 Order of pole (given) = 3 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) = 1.451589490492089 y[1] (numeric) = 1.451589490492088 absolute error = 1.110223024625157e-15 relative error = 7.648326416642701e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.83 Order of pole (given) = 3 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) = 1.48720999405116 y[1] (numeric) = 1.487209994051159 absolute error = 1.332267629550188e-15 relative error = 8.958167541095461e-14 % Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 0.82 Order of pole (given) = 3 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) = 1.524157902758726 y[1] (numeric) = 1.524157902758725 absolute error = 1.77635683940025e-15 relative error = 1.165467722330504e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.81 Order of pole (given) = 3 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 Radius of convergence (six term test) for eq 1 = 0.3285 Order of pole (six term test) = 8.814e-11 TOP MAIN SOLVE Loop x[1] = -0.7999999999999998 y[1] (analytic) = 1.562500000000001 y[1] (numeric) = 1.562499999999998 absolute error = 2.220446049250313e-15 relative error = 1.4210854715202e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.8 Order of pole (given) = 3 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) = 1.602307322544465 y[1] (numeric) = 1.602307322544462 absolute error = 2.442490654175344e-15 relative error = 1.524358417270832e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.79 Order of pole (given) = 3 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) = 1.643655489809337 y[1] (numeric) = 1.643655489809334 absolute error = 2.664535259100376e-15 relative error = 1.621103251636668e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.78 Order of pole (given) = 3 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) = 1.686625063248441 y[1] (numeric) = 1.686625063248438 absolute error = 2.886579864025407e-15 relative error = 1.711453201380663e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.77 Order of pole (given) = 3 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) = 1.731301939058173 y[1] (numeric) = 1.73130193905817 absolute error = 3.108624468950438e-15 relative error = 1.795541493265772e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.76 Order of pole (given) = 3 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) = 1.777777777777779 y[1] (numeric) = 1.777777777777775 absolute error = 3.552713678800501e-15 relative error = 1.998401444325281e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.75 Order of pole (given) = 3 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7399999999999998 y[1] (analytic) = 1.826150474799125 y[1] (numeric) = 1.826150474799121 absolute error = 3.552713678800501e-15 relative error = 1.945466010511153e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.74 Order of pole (given) = 3 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) = 1.876524676299494 y[1] (numeric) = 1.87652467629949 absolute error = 3.996802888650564e-15 relative error = 2.129896259361884e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.73 Order of pole (given) = 3 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) = 1.929012345679014 y[1] (numeric) = 1.929012345679009 absolute error = 4.218847493575595e-15 relative error = 2.187050540669587e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.72 Order of pole (given) = 3 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7099999999999997 y[1] (analytic) = 1.983733386232892 y[1] (numeric) = 1.983733386232887 absolute error = 4.440892098500626e-15 relative error = 2.238653706854164e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 0.71 Order of pole (given) = 3 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 * 2.0 / 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 %