##############ECHO OF PROBLEM################# ##############temp/sing1postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=20; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-2.0; x_end=-1.5; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=500; glob_max_h=0.5; glob_type_given_pole=4; array_given_rad_poles[1][1]=0.0; array_given_rad_poles[1][2]=0.001; array_given_ord_poles[1][1]=1.0; 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=1000000000; 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 + 0.000001)) ; } /* 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 = 0.5 estimated_steps = 500000 step_error = 2e-16 est_needed_step_err = 2e-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 = 6.484894657593405e-101 estimated_step_error = 6.484894657593405e-101 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 = 4.249941687783492e-96 estimated_step_error = 4.249941687783492e-96 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 = 2.785243259044777e-91 estimated_step_error = 2.785243259044777e-91 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 = 1.825338954958387e-86 estimated_step_error = 1.825338954958387e-86 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 = 1.196256670772253e-81 estimated_step_error = 1.196256670772253e-81 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 = 7.839820921607223e-77 estimated_step_error = 7.839820921607223e-77 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 = 5.137948560927475e-72 estimated_step_error = 5.137948560927475e-72 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 = 3.367263015153551e-67 estimated_step_error = 3.367263015153551e-67 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 = 2.206844265079019e-62 estimated_step_error = 2.206844265079019e-62 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 = 1.446375477196556e-57 estimated_step_error = 1.446375477196556e-57 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 = 9.480251350755155e-53 estimated_step_error = 9.480251350755155e-53 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.214662514172606e-48 estimated_step_error = 6.214662514172606e-48 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.075051566311024e-43 estimated_step_error = 4.075051566311024e-43 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.673527639981127e-38 estimated_step_error = 2.673527639981127e-38 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.755938967328436e-33 estimated_step_error = 1.755938967328436e-33 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.155806442194792e-28 estimated_step_error = 1.155806442194792e-28 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.64154872314529e-24 estimated_step_error = 7.64154872314529e-24 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.097942655829754e-19 estimated_step_error = 5.097942655829754e-19 best_h = 0.262144 opt_iter = 19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.465429033624368e-14 estimated_step_error = 3.465429033624368e-14 best_h = 0.131072 START of Soultion TOP MAIN SOLVE Loop x[1] = -2 y[1] (analytic) = 0.2499999375000156 y[1] (numeric) = 0.2499999375000156 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 2 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.99 y[1] (analytic) = 0.2525188120201984 y[1] (numeric) = 0.2525188120201985 absolute error = 5.551115123125783e-17 relative error = 2.198297655020554e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.99 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.99 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.99 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.98 y[1] (analytic) = 0.2550759475880146 y[1] (numeric) = 0.2550759475880146 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.98 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.98 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.98 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.97 y[1] (analytic) = 0.2576721230456536 y[1] (numeric) = 0.2576721230456536 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.97 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.97 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.97 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.96 y[1] (analytic) = 0.260308137154275 y[1] (numeric) = 0.260308137154275 absolute error = 5.551115123125783e-17 relative error = 2.132516940811513e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.96 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.96 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.96 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.95 y[1] (analytic) = 0.2629848092084657 y[1] (numeric) = 0.2629848092084657 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.95 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.95 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.94 y[1] (analytic) = 0.2657029796729249 y[1] (numeric) = 0.2657029796729249 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.94 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.94 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.94 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.93 y[1] (analytic) = 0.2684635108423016 y[1] (numeric) = 0.2684635108423016 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.93 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.93 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.93 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.92 y[1] (analytic) = 0.2712672875251499 y[1] (numeric) = 0.2712672875251499 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.92 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.92 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.92 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.91 y[1] (analytic) = 0.2741152177530172 y[1] (numeric) = 0.2741152177530173 absolute error = 5.551115123125783e-17 relative error = 2.025102863179029e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.91 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.91 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.91 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (analytic) = 0.2770082335157248 y[1] (numeric) = 0.2770082335157248 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.9 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.9 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.89 y[1] (analytic) = 0.2799472915239519 y[1] (numeric) = 0.2799472915239519 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.89 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.89 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.89 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.88 y[1] (analytic) = 0.2829333740002903 y[1] (numeric) = 0.2829333740002903 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.88 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.88 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.88 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.87 y[1] (analytic) = 0.2859674894999887 y[1] (numeric) = 0.2859674894999887 absolute error = 5.551115123125783e-17 relative error = 1.941170002517367e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.87 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.87 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.87 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.86 y[1] (analytic) = 0.289050673762668 y[1] (numeric) = 0.289050673762668 absolute error = 5.551115123125783e-17 relative error = 1.920464343108108e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.86 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.86 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.86 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.85 y[1] (analytic) = 0.2921839905963505 y[1] (numeric) = 0.2921839905963504 absolute error = 5.551115123125783e-17 relative error = 1.899869706001311e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.85 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.85 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.84 y[1] (analytic) = 0.2953685327952113 y[1] (numeric) = 0.2953685327952112 absolute error = 5.551115123125783e-17 relative error = 1.879386091196977e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.84 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.84 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.84 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.83 y[1] (analytic) = 0.298605423092531 y[1] (numeric) = 0.298605423092531 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.83 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.83 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.83 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.82 y[1] (analytic) = 0.3018958151504 y[1] (numeric) = 0.3018958151504 absolute error = 5.551115123125783e-17 relative error = 1.838751928495696e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.82 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.82 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.82 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.81 y[1] (analytic) = 0.3052408945878042 y[1] (numeric) = 0.3052408945878042 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.81 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.81 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.81 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.8 y[1] (analytic) = 0.3086418800488025 y[1] (numeric) = 0.3086418800488024 absolute error = 5.551115123125783e-17 relative error = 1.798561855004266e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.8 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.79 y[1] (analytic) = 0.3121000243125919 y[1] (numeric) = 0.3121000243125919 absolute error = 5.551115123125783e-17 relative error = 1.778633351712244e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.79 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.79 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.79 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.78 y[1] (analytic) = 0.3156166154473503 y[1] (numeric) = 0.3156166154473503 absolute error = 5.551115123125783e-17 relative error = 1.758815870722685e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.78 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.78 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.78 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.77 y[1] (analytic) = 0.3191929780098382 y[1] (numeric) = 0.3191929780098381 absolute error = 5.551115123125783e-17 relative error = 1.739109412035588e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.77 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.77 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.77 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.76 y[1] (analytic) = 0.3228304742928479 y[1] (numeric) = 0.3228304742928479 absolute error = 5.551115123125783e-17 relative error = 1.719513975650955e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.76 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.76 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.76 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.75 y[1] (analytic) = 0.3265305056226921 y[1] (numeric) = 0.326530505622692 absolute error = 1.110223024625157e-16 relative error = 3.400059123137566e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.75 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.75 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.74 y[1] (analytic) = 0.330294513709039 y[1] (numeric) = 0.330294513709039 absolute error = 5.551115123125783e-17 relative error = 1.680656169789074e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.74 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.74 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.74 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.73 y[1] (analytic) = 0.3341239820495233 y[1] (numeric) = 0.3341239820495232 absolute error = 5.551115123125783e-17 relative error = 1.661393800311827e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.73 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.73 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.73 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.72 y[1] (analytic) = 0.3380204373916856 y[1] (numeric) = 0.3380204373916856 absolute error = 5.551115123125783e-17 relative error = 1.642242453137044e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.72 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.72 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.72 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.71 y[1] (analytic) = 0.3419854512549328 y[1] (numeric) = 0.3419854512549327 absolute error = 5.551115123125783e-17 relative error = 1.623202128264722e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.71 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.71 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.71 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.7 y[1] (analytic) = 0.3460206415153491 y[1] (numeric) = 0.346020641515349 absolute error = 5.551115123125783e-17 relative error = 1.604272825694863e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.7 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.7 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.69 y[1] (analytic) = 0.3501276740563447 y[1] (numeric) = 0.3501276740563447 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.69 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.69 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.69 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.68 y[1] (analytic) = 0.3543082644882851 y[1] (numeric) = 0.3543082644882851 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.68 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.68 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.68 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.67 y[1] (analytic) = 0.3585641799404139 y[1] (numeric) = 0.3585641799404139 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.67 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.67 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.67 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.66 y[1] (analytic) = 0.3628972409285671 y[1] (numeric) = 0.362897240928567 absolute error = 5.551115123125783e-17 relative error = 1.529665838440053e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.66 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.66 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.66 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.65 y[1] (analytic) = 0.3673093233023607 y[1] (numeric) = 0.3673093233023607 absolute error = 5.551115123125783e-17 relative error = 1.511291647382506e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.65 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.65 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.64 y[1] (analytic) = 0.3718023602757436 y[1] (numeric) = 0.3718023602757436 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.64 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.64 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.64 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.63 y[1] (analytic) = 0.3763783445450171 y[1] (numeric) = 0.376378344545017 absolute error = 5.551115123125783e-17 relative error = 1.474876332174801e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.63 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.63 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.63 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.62 y[1] (analytic) = 0.3810393304986549 y[1] (numeric) = 0.3810393304986548 absolute error = 5.551115123125783e-17 relative error = 1.456835208024642e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.62 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.62 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.62 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.61 y[1] (analytic) = 0.3857874365234998 y[1] (numeric) = 0.3857874365234998 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.61 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.61 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.61 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.6 y[1] (analytic) = 0.3906248474121691 y[1] (numeric) = 0.3906248474121691 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.6 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.59 y[1] (analytic) = 0.3955538168767784 y[1] (numeric) = 0.3955538168767784 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.59 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.59 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.59 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.58 y[1] (analytic) = 0.4005766701743833 y[1] (numeric) = 0.4005766701743832 absolute error = 5.551115123125783e-17 relative error = 1.385780934448632e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.58 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.58 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.58 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.57 y[1] (analytic) = 0.4056958068498493 y[1] (numeric) = 0.4056958068498493 absolute error = 5.551115123125783e-17 relative error = 1.368294921810786e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.57 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.57 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.57 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.56 y[1] (analytic) = 0.410913703602193 y[1] (numeric) = 0.410913703602193 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.56 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.56 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.56 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.55 y[1] (analytic) = 0.4162329172807838 y[1] (numeric) = 0.4162329172807838 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.55 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.55 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.54 y[1] (analytic) = 0.4216560880181787 y[1] (numeric) = 0.4216560880181786 absolute error = 5.551115123125783e-17 relative error = 1.316503017712022e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.54 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.54 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.54 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.53 y[1] (analytic) = 0.427185942506753 y[1] (numeric) = 0.4271859425067529 absolute error = 5.551115123125783e-17 relative error = 1.299461094284026e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.53 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.53 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.53 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.52 y[1] (analytic) = 0.432825297426724 y[1] (numeric) = 0.4328252974267239 absolute error = 5.551115123125783e-17 relative error = 1.282530193158492e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.52 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.52 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.52 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.51 y[1] (analytic) = 0.4385770630336114 y[1] (numeric) = 0.4385770630336114 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.51 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.51 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.51 Order of pole (six term test) = 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; Iterations = 50 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 102 %