##############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_type_given_pole=1; array_given_rad_poles[1][1]=0.0; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=4.0; 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=100000000; glob_max_minutes=10.0; 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 = 9.128709291752769e-15 est_needed_step_err = 9.128709291752769e-15 opt_iter = 1 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) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 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 = 9.128709291752769e-15 est_needed_step_err = 9.128709291752769e-15 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 Double H and LOOP opt_iter = 2 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) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.3 estimated_steps = 150000 step_error = 1.290994448735806e-14 est_needed_step_err = 1.290994448735806e-14 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 Double H and LOOP opt_iter = 3 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) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.3 estimated_steps = 75000.00000000001 step_error = 1.825741858350554e-14 est_needed_step_err = 1.825741858350554e-14 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 Double H and LOOP opt_iter = 4 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) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.3 estimated_steps = 37500.00000000001 step_error = 2.581988897471611e-14 est_needed_step_err = 2.581988897471611e-14 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 Double H and LOOP opt_iter = 5 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) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.3 estimated_steps = 18750 step_error = 3.651483716701107e-14 est_needed_step_err = 3.651483716701107e-14 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 Double H and LOOP opt_iter = 6 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) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.3 estimated_steps = 9375.000000000002 step_error = 5.163977794943222e-14 est_needed_step_err = 5.163977794943222e-14 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 Double H and LOOP opt_iter = 7 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) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.3 estimated_steps = 4687.500000000001 step_error = 7.302967433402215e-14 est_needed_step_err = 7.302967433402215e-14 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 Double H and LOOP opt_iter = 8 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) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.3 estimated_steps = 2343.75 step_error = 1.032795558988644e-13 est_needed_step_err = 1.032795558988644e-13 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 Double H and LOOP opt_iter = 9 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) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.3 estimated_steps = 1171.875 step_error = 1.460593486680443e-13 est_needed_step_err = 1.460593486680443e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.233372088680488e-57 estimated_step_error = 2.233372088680488e-57 Double H and LOOP opt_iter = 10 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) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.3 estimated_steps = 585.9375000000001 step_error = 2.065591117977289e-13 est_needed_step_err = 2.065591117977289e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.463839103064355e-52 estimated_step_error = 1.463839103064355e-52 Double H and LOOP opt_iter = 11 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) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.3 estimated_steps = 292.9687500000001 step_error = 2.921186973360886e-13 est_needed_step_err = 2.921186973360886e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.595728514958766e-48 estimated_step_error = 9.595728514958766e-48 Double H and LOOP opt_iter = 12 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) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.3 estimated_steps = 146.484375 step_error = 4.131182235954578e-13 est_needed_step_err = 4.131182235954578e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.291689970870765e-43 estimated_step_error = 6.291689970870765e-43 Double H and LOOP opt_iter = 13 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) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.3 estimated_steps = 73.24218750000001 step_error = 5.842373946721772e-13 est_needed_step_err = 5.842373946721772e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.127303566141865e-38 estimated_step_error = 4.127303566141865e-38 Double H and LOOP opt_iter = 14 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) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.3 estimated_steps = 36.62109375000001 step_error = 8.262364471909155e-13 est_needed_step_err = 8.262364471909155e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.710103663121732e-33 estimated_step_error = 2.710103663121732e-33 Double H and LOOP opt_iter = 15 SETTING H FOR DISPLAY INTERVAL 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 = 0.6104 Order of pole (three term test) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = -1 y[1] (analytic) = -1 y[1] (numeric) = -1 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.01 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) = 0 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) = -1.030610152117651 absolute error = 1.071343014302784e-11 relative error = 1.039523055434976e-09 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 11 h = 0.01 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) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.98 y[1] (analytic) = -1.062482469039261 y[1] (numeric) = -1.062482469016818 absolute error = 2.244315844279754e-11 relative error = 2.11233211810935e-09 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 11 h = 0.01 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) = 0 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) = -1.09568268149467 absolute error = 3.529798675572238e-11 relative error = 3.22155194663054e-09 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 11 h = 0.01 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) = 3.244e-14 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) = -1.130280671246898 absolute error = 4.939892939148649e-11 relative error = 4.370501119410618e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 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) = 4.658e-14 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) = -1.166350779932203 absolute error = 6.488143355909415e-11 relative error = 5.562771909772834e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 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) = 3.331e-14 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) = -1.203972144818558 absolute error = 8.189782185752392e-11 relative error = 6.802302046970964e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 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) = 4.749e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9299999999999999 y[1] (analytic) = -1.24322906371176 y[1] (numeric) = -1.243229063611141 absolute error = 1.006190686325681e-10 relative error = 8.093365218808653e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 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) = 0 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) = -1.284211391347491 absolute error = 1.212363542890671e-10 relative error = 9.440529424864505e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 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) = 4.773e-14 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) = -1.327014972565971 absolute error = 1.439659502722179e-10 relative error = 1.084885651125855e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 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) = 6.728e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8999999999999999 y[1] (analytic) = -1.371742112482853 y[1] (numeric) = -1.371742112313802 absolute error = 1.690509954244135e-10 relative error = 1.232381756643974e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 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) = 2.362e-14 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) = -1.418502089966064 absolute error = 1.967659368773411e-10 relative error = 1.387138857544823e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 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) = 0 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) = -1.467411720283474 absolute error = 2.274205268548712e-10 relative error = 1.549807212768427e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 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) = 4.603e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8699999999999999 y[1] (analytic) = -1.518595966912831 y[1] (numeric) = -1.518595966651466 absolute error = 2.613653737881805e-10 relative error = 1.721098827356382e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 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) = 0 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) = -1.572188612024446 absolute error = 2.989977154754797e-10 relative error = 1.901792909144717e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 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) = 4.411e-14 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) = -1.628332993756526 absolute error = 3.407678583755569e-10 relative error = 2.092740610248888e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 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) = 0 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) = -1.687182809244603 absolute error = 3.871873932581593e-10 relative error = 2.29487516733684e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 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) = 4.155e-14 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) = -1.74890300015404 absolute error = 4.388387431220053e-10 relative error = 2.509222884135019e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 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) = 5.665e-14 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) = -1.81367072395625 absolute error = 4.963849331574011e-10 relative error = 2.736907678251298e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 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) = 3.844e-14 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) = -1.881676422598338 absolute error = 5.605833575117458e-10 relative error = 2.979169800993996e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 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) = 0 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) = -1.953124999367701 absolute error = 6.322999901442472e-10 relative error = 3.237375949538543e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 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) = 3.488e-14 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) = -2.028237116432368 absolute error = 7.12524705903661e-10 relative error = 3.513024684740349e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 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) = 1.166e-13 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) = -2.107250627158294 absolute error = 8.023945952118083e-10 relative error = 3.807779599469538e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 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] (analytic) = -2.190422160062911 y[1] (numeric) = -2.190422159159696 absolute error = 9.032148362564385e-10 relative error = 4.123473788406603e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 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) = 4.107e-14 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) = -2.278028866165318 absolute error = 1.016488671012894e-09 relative error = 4.462141308465558e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 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) = 8.108e-14 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) = -2.370370369226424 absolute error = 1.14394893557801e-09 relative error = 4.826034571969724e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 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) = 3.538e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7399999999999998 y[1] (analytic) = -2.46777091189071 y[1] (numeric) = -2.467770910603113 absolute error = 1.28759714002058e-09 relative error = 5.217652634676989e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 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) = 4.605e-14 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) = -2.570581746905723 absolute error = 1.449750097748392e-09 relative error = 5.639774337757858e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 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) = 5.959e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7199999999999998 y[1] (analytic) = -2.679183813443075 y[1] (numeric) = -2.679183811809981 absolute error = 1.63309410439183e-09 relative error = 6.095491082760413e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 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) = 3.833e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7099999999999997 y[1] (analytic) = -2.79399068483506 y[1] (numeric) = -2.793990682994308 absolute error = 1.840752439363769e-09 relative error = 6.58825546325125e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 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) = 4.9e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ; Iterations = 30 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 103.3 %