##############ECHO OF PROBLEM################# ##############temp/div_c_lin_backpostode.ode################# diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=3.1; x_end=2.5; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_display_interval=0.1; glob_type_given_pole=1; array_given_rad_poles[1][1]=-1.5; array_given_rad_poles[1][2]=0.0; 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=100000000; glob_max_minutes=10.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(10.0* ln(0.2* x + 0.3)); } /* 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 = -0.6000000000000001 estimated_steps = 600000.0000000001 step_error = 4.303314829119352e-15 est_needed_step_err = 4.303314829119352e-15 opt_iter = 1 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.6000000000000001 estimated_steps = 600000.0000000001 step_error = 4.303314829119352e-15 est_needed_step_err = 4.303314829119352e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.6000000000000001 estimated_steps = 300000.0000000001 step_error = 6.085806194501845e-15 est_needed_step_err = 6.085806194501845e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.6000000000000001 estimated_steps = 150000 step_error = 8.606629658238704e-15 est_needed_step_err = 8.606629658238704e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.6000000000000001 estimated_steps = 75000.00000000001 step_error = 1.217161238900369e-14 est_needed_step_err = 1.217161238900369e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.6000000000000001 estimated_steps = 37500.00000000001 step_error = 1.721325931647741e-14 est_needed_step_err = 1.721325931647741e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.6000000000000001 estimated_steps = 18750 step_error = 2.434322477800738e-14 est_needed_step_err = 2.434322477800738e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.6000000000000001 estimated_steps = 9375.000000000002 step_error = 3.442651863295482e-14 est_needed_step_err = 3.442651863295482e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 8 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.6000000000000001 estimated_steps = 4687.500000000001 step_error = 4.868644955601476e-14 est_needed_step_err = 4.868644955601476e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 9 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.6000000000000001 estimated_steps = 2343.75 step_error = 6.885303726590963e-14 est_needed_step_err = 6.885303726590963e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 10 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.6000000000000001 estimated_steps = 1171.875 step_error = 9.737289911202953e-14 est_needed_step_err = 9.737289911202953e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 11 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.6000000000000001 estimated_steps = 585.9375000000001 step_error = 1.377060745318193e-13 est_needed_step_err = 1.377060745318193e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 12 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.6000000000000001 estimated_steps = 292.9687500000001 step_error = 1.947457982240591e-13 est_needed_step_err = 1.947457982240591e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 13 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.6000000000000001 estimated_steps = 146.484375 step_error = 2.754121490636385e-13 est_needed_step_err = 2.754121490636385e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 14 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.8338160893905089 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.6000000000000001 estimated_steps = 73.24218750000001 step_error = 3.894915964481181e-13 est_needed_step_err = 3.894915964481181e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 15 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (analytic) = -0.8338160893905089 y[1] (numeric) = -0.8338160893905089 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 = 4.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (analytic) = -0.8555788836164642 y[1] (numeric) = -0.8555788836164639 absolute error = 2.220446049250313e-16 relative error = 2.595255787361959e-14 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 4.59 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.080000000000001 y[1] (analytic) = -0.8773891430800662 y[1] (numeric) = -0.8773891430800658 absolute error = 4.440892098500626e-16 relative error = 5.061485127238886e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 4.58 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.070000000000001 y[1] (analytic) = -0.8992470752798688 y[1] (numeric) = -0.8992470752798681 absolute error = 6.661338147750939e-16 relative error = 7.407683973481659e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 4.57 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.060000000000001 y[1] (analytic) = -0.921152889078055 y[1] (numeric) = -0.9211528890780541 absolute error = 8.881784197001252e-16 relative error = 9.642030440669489e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 4.56 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.050000000000001 y[1] (analytic) = -0.9431067947124093 y[1] (numeric) = -0.9431067947124105 absolute error = 1.221245327087672e-15 relative error = 1.294917324246485e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.040000000000001 y[1] (analytic) = -0.9651090038084336 y[1] (numeric) = -0.9651090038084347 absolute error = 1.110223024625157e-15 relative error = 1.150360239355436e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.54 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.030000000000002 y[1] (analytic) = -0.9871597293915733 y[1] (numeric) = -0.9871597293915741 absolute error = 8.881784197001252e-16 relative error = 8.997312119362343e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 4.53 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.020000000000002 y[1] (analytic) = -1.009259185899602 y[1] (numeric) = -1.009259185899602 absolute error = 6.661338147750939e-16 relative error = 6.600225433483042e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 4.52 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.010000000000002 y[1] (analytic) = -1.03140758919513 y[1] (numeric) = -1.03140758919513 absolute error = 4.440892098500626e-16 relative error = 4.305661646300397e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 4.51 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.000000000000002 y[1] (analytic) = -1.053605156578256 y[1] (numeric) = -1.053605156578259 absolute error = 2.886579864025407e-15 relative error = 2.739716910080448e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.990000000000002 y[1] (analytic) = -1.075852106799368 y[1] (numeric) = -1.075852106799371 absolute error = 2.664535259100376e-15 relative error = 2.476674295900483e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.49 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.980000000000003 y[1] (analytic) = -1.098148660072059 y[1] (numeric) = -1.098148660072062 absolute error = 2.442490654175344e-15 relative error = 2.224189440813114e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.48 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.970000000000003 y[1] (analytic) = -1.120495038086223 y[1] (numeric) = -1.120495038086225 absolute error = 2.220446049250313e-15 relative error = 1.981665222759736e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.47 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.960000000000003 y[1] (analytic) = -1.14289146402127 y[1] (numeric) = -1.142891464021272 absolute error = 1.77635683940025e-15 relative error = 1.554265558297311e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.46 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.950000000000003 y[1] (analytic) = -1.165338162559509 y[1] (numeric) = -1.165338162559511 absolute error = 1.554312234475219e-15 relative error = 1.333786435914345e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.940000000000003 y[1] (analytic) = -1.187835359899661 y[1] (numeric) = -1.187835359899665 absolute error = 3.996802888650564e-15 relative error = 3.36477850683632e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.44 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.930000000000004 y[1] (analytic) = -1.210383283770552 y[1] (numeric) = -1.210383283770556 absolute error = 3.774758283725532e-15 relative error = 3.118647071832082e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.43 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.920000000000004 y[1] (analytic) = -1.232982163444927 y[1] (numeric) = -1.232982163444931 absolute error = 3.552713678800501e-15 relative error = 2.881399085996744e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.42 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.910000000000004 y[1] (analytic) = -1.255632229753449 y[1] (numeric) = -1.255632229753452 absolute error = 3.33066907387547e-15 relative error = 2.652583292266612e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.41 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.900000000000004 y[1] (analytic) = -1.27833371509884 y[1] (numeric) = -1.278333715098843 absolute error = 3.108624468950438e-15 relative error = 2.431778519359541e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.890000000000005 y[1] (analytic) = -1.301086853470192 y[1] (numeric) = -1.301086853470198 absolute error = 5.329070518200751e-15 relative error = 4.095860705983868e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.39 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.880000000000005 y[1] (analytic) = -1.323891880457445 y[1] (numeric) = -1.32389188045745 absolute error = 4.884981308350689e-15 relative error = 3.689864240773785e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.38 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.870000000000005 y[1] (analytic) = -1.346749033266005 y[1] (numeric) = -1.346749033266009 absolute error = 4.662936703425657e-15 relative error = 3.462364990244364e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.37 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.860000000000005 y[1] (analytic) = -1.369658550731563 y[1] (numeric) = -1.369658550731567 absolute error = 4.440892098500626e-15 relative error = 3.242335176258823e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.36 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.850000000000005 y[1] (analytic) = -1.392620673335065 y[1] (numeric) = -1.392620673335069 absolute error = 3.996802888650564e-15 relative error = 2.869986756033839e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.840000000000006 y[1] (analytic) = -1.415635643217855 y[1] (numeric) = -1.415635643217861 absolute error = 6.217248937900877e-15 relative error = 4.391842609845966e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.34 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.830000000000006 y[1] (analytic) = -1.438703704197005 y[1] (numeric) = -1.438703704197011 absolute error = 5.995204332975845e-15 relative error = 4.167087577161689e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.33 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.820000000000006 y[1] (analytic) = -1.4618251017808 y[1] (numeric) = -1.461825101780806 absolute error = 5.773159728050814e-15 relative error = 3.949282113857486e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.32 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.810000000000006 y[1] (analytic) = -1.485000083184425 y[1] (numeric) = -1.485000083184431 absolute error = 5.773159728050814e-15 relative error = 3.887649430746754e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.31 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.800000000000006 y[1] (analytic) = -1.508228897345822 y[1] (numeric) = -1.508228897345828 absolute error = 5.329070518200751e-15 relative error = 3.533330071833816e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.790000000000007 y[1] (analytic) = -1.531511794941731 y[1] (numeric) = -1.531511794941739 absolute error = 7.549516567451064e-15 relative error = 4.929453754378886e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.29 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.780000000000007 y[1] (analytic) = -1.554849028403933 y[1] (numeric) = -1.55484902840394 absolute error = 7.327471962526033e-15 relative error = 4.712658160804044e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.28 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.770000000000007 y[1] (analytic) = -1.578240851935655 y[1] (numeric) = -1.578240851935662 absolute error = 7.105427357601002e-15 relative error = 4.502118513081481e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.27 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.760000000000007 y[1] (analytic) = -1.601687521528196 y[1] (numeric) = -1.601687521528203 absolute error = 6.883382752675971e-15 relative error = 4.297581557049543e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.26 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.750000000000008 y[1] (analytic) = -1.625189294977732 y[1] (numeric) = -1.625189294977739 absolute error = 6.439293542825908e-15 relative error = 3.962180628881226e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.740000000000008 y[1] (analytic) = -1.64874643190232 y[1] (numeric) = -1.648746431902329 absolute error = 8.881784197001252e-15 relative error = 5.386992217325661e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.24 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.730000000000008 y[1] (analytic) = -1.672359193759118 y[1] (numeric) = -1.672359193759127 absolute error = 8.43769498715119e-15 relative error = 5.045384399857899e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.23 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.720000000000008 y[1] (analytic) = -1.69602784386178 y[1] (numeric) = -1.696027843861788 absolute error = 8.215650382226158e-15 relative error = 4.84405395345367e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.22 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.710000000000008 y[1] (analytic) = -1.719752647398084 y[1] (numeric) = -1.719752647398092 absolute error = 7.993605777301127e-15 relative error = 4.648113662970735e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.21 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.700000000000009 y[1] (analytic) = -1.743533871447758 y[1] (numeric) = -1.743533871447766 absolute error = 7.771561172376096e-15 relative error = 4.457361740797679e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.690000000000009 y[1] (analytic) = -1.767371785000518 y[1] (numeric) = -1.767371785000528 absolute error = 9.992007221626409e-15 relative error = 5.653596660548409e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.19 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.680000000000009 y[1] (analytic) = -1.791266658974332 y[1] (numeric) = -1.791266658974342 absolute error = 9.769962616701378e-15 relative error = 5.45422010048219e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.18 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.670000000000009 y[1] (analytic) = -1.815218766233881 y[1] (numeric) = -1.81521876623389 absolute error = 9.547918011776346e-15 relative error = 5.259926896627374e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.17 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.660000000000009 y[1] (analytic) = -1.839228381609262 y[1] (numeric) = -1.839228381609271 absolute error = 8.881784197001252e-15 relative error = 4.829081742002042e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.16 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.65000000000001 y[1] (analytic) = -1.863295781914912 y[1] (numeric) = -1.863295781914921 absolute error = 8.881784197001252e-15 relative error = 4.766706543967715e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.64000000000001 y[1] (analytic) = -1.887421245968749 y[1] (numeric) = -1.88742124596876 absolute error = 1.110223024625157e-14 relative error = 5.882221719165385e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.14 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.63000000000001 y[1] (analytic) = -1.911605054611565 y[1] (numeric) = -1.911605054611576 absolute error = 1.088018564132653e-14 relative error = 5.691649336812081e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.13 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.62000000000001 y[1] (analytic) = -1.935847490726629 y[1] (numeric) = -1.935847490726639 absolute error = 1.043609643147647e-14 relative error = 5.390970353537116e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.12 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.610000000000011 y[1] (analytic) = -1.960148839259546 y[1] (numeric) = -1.960148839259556 absolute error = 1.021405182655144e-14 relative error = 5.210855227917202e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.11 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.600000000000011 y[1] (analytic) = -1.984509387238357 y[1] (numeric) = -1.984509387238367 absolute error = 9.547918011776346e-15 relative error = 4.811223405228244e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.590000000000011 y[1] (analytic) = -2.008929423793872 y[1] (numeric) = -2.008929423793884 absolute error = 1.199040866595169e-14 relative error = 5.968556447994947e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.09 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.580000000000011 y[1] (analytic) = -2.033409240180272 y[1] (numeric) = -2.033409240180284 absolute error = 1.199040866595169e-14 relative error = 5.896702163549074e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.08 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.570000000000011 y[1] (analytic) = -2.05794912979594 y[1] (numeric) = -2.057949129795951 absolute error = 1.154631945610163e-14 relative error = 5.61059517406367e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.07 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.560000000000012 y[1] (analytic) = -2.082549388204563 y[1] (numeric) = -2.082549388204574 absolute error = 1.110223024625157e-14 relative error = 5.331076568524109e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.06 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.550000000000012 y[1] (analytic) = -2.107210313156498 y[1] (numeric) = -2.107210313156509 absolute error = 1.06581410364015e-14 relative error = 5.057938910917786e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.540000000000012 y[1] (analytic) = -2.131932204610386 y[1] (numeric) = -2.131932204610399 absolute error = 1.287858708565182e-14 relative error = 6.040805170915554e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.04 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.530000000000012 y[1] (analytic) = -2.156715364755057 y[1] (numeric) = -2.156715364755069 absolute error = 1.287858708565182e-14 relative error = 5.971389315490164e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.03 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.520000000000012 y[1] (analytic) = -2.181560098031676 y[1] (numeric) = -2.181560098031688 absolute error = 1.243449787580175e-14 relative error = 5.699819082234244e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.02 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.510000000000013 y[1] (analytic) = -2.206466711156195 y[1] (numeric) = -2.206466711156207 absolute error = 1.199040866595169e-14 relative error = 5.43421235649129e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4.01 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.500000000000013 y[1] (analytic) = -2.231435513142066 y[1] (numeric) = -2.231435513142078 absolute error = 1.154631945610163e-14 relative error = 5.174390829624894e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = -0.01 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ; Iterations = 61 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Expected Time Remaining = 0.0 Seconds Optimized Time Remaining = 0.0 Seconds Expected Total Time = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 0 %