##############ECHO OF PROBLEM################# ##############temp/lin_tanpostode.ode################# diff ( y , x , 1 ) = tan ( 2.0 * x + 3.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-1.0; x_end=-0.9; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=0.0001; glob_type_given_pole=1; array_given_rad_poles[1][1]=-0.714601837; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=0.0; 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(ln(1.0 + expt(tan(2.0 * x + 3.0),2))/4.0); } /* 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 = 0.0001 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.09999999999999998 estimated_steps = 999.9999999999998 step_error = 1.05409255338946e-13 est_needed_step_err = 1.05409255338946e-13 opt_iter = 1 Radius of convergence (given) for eq 1 = 0.2854 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2854 Order of pole (three term test) = 3.425e-12 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.3078132351930071 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.0001 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.09999999999999998 estimated_steps = 999.9999999999998 step_error = 1.05409255338946e-13 est_needed_step_err = 1.05409255338946e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.769104887809524e-92 estimated_step_error = 2.769104887809524e-92 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 0.2854 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2854 Order of pole (three term test) = 3.425e-12 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.3078132351930071 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.0002 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.09999999999999998 estimated_steps = 499.9999999999999 step_error = 1.49071198499986e-13 est_needed_step_err = 1.49071198499986e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.858628446547863e-84 estimated_step_error = 1.858628446547863e-84 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 0.2854 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2854 Order of pole (three term test) = 3.425e-12 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.3078132351930071 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.0004 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.09999999999999998 estimated_steps = 249.9999999999999 step_error = 2.10818510677892e-13 est_needed_step_err = 2.10818510677892e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.247725574673143e-76 estimated_step_error = 1.247725574673143e-76 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 0.2854 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2854 Order of pole (three term test) = 3.425e-12 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.3078132351930071 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.0008 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.09999999999999998 estimated_steps = 125 step_error = 2.98142396999972e-13 est_needed_step_err = 2.98142396999972e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.379002748596237e-69 estimated_step_error = 8.379002748596237e-69 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 0.2854 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2854 Order of pole (three term test) = 3.425e-12 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.3078132351930071 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.0016 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.09999999999999998 estimated_steps = 62.49999999999999 step_error = 4.21637021355784e-13 est_needed_step_err = 4.21637021355784e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.630663247984856e-61 estimated_step_error = 5.630663247984856e-61 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 0.2854 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2854 Order of pole (three term test) = 3.425e-12 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.3078132351930071 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.0032 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.09999999999999998 estimated_steps = 31.24999999999999 step_error = 5.962847939999441e-13 est_needed_step_err = 5.962847939999441e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.788929326532097e-53 estimated_step_error = 3.788929326532097e-53 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 0.2854 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2854 Order of pole (three term test) = 3.425e-12 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.3078132351930071 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.0064 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.09999999999999998 estimated_steps = 15.625 step_error = 8.43274042711568e-13 est_needed_step_err = 8.43274042711568e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.556584513439701e-45 estimated_step_error = 2.556584513439701e-45 Double H and LOOP opt_iter = 8 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 0.2854 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.223 Order of pole (three term test) = 3.425e-12 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = -1 y[1] (analytic) = 0.3078132351930071 y[1] (numeric) = 0.3078132351930071 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 = 0.2854 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2854 Order of pole (three term test) = 3.274e-12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.99 y[1] (analytic) = 0.3237371720088514 y[1] (numeric) = 0.3237371720088514 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 = 0.2754 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2754 Order of pole (three term test) = 1.269e-12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.98 y[1] (analytic) = 0.3403917067162167 y[1] (numeric) = 0.3403917067162167 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.2654 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2654 Order of pole (three term test) = 4.21e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.97 y[1] (analytic) = 0.3578272075077493 y[1] (numeric) = 0.3578272075077493 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.2554 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2554 Order of pole (three term test) = 1.151e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.96 y[1] (analytic) = 0.3761001320103593 y[1] (numeric) = 0.3761001320103592 absolute error = 5.551115123125783e-17 relative error = 1.475967342381279e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.2454 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2454 Order of pole (three term test) = 2.933e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.95 y[1] (analytic) = 0.3952740386271159 y[1] (numeric) = 0.3952740386271158 absolute error = 1.110223024625157e-16 relative error = 2.808742583958295e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.2354 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2354 Order of pole (three term test) = 8.654e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9399999999999999 y[1] (analytic) = 0.415420817612529 y[1] (numeric) = 0.4154208176125289 absolute error = 1.110223024625157e-16 relative error = 2.672526213312408e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.2254 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2254 Order of pole (three term test) = 1.88e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9299999999999999 y[1] (analytic) = 0.4366222017597863 y[1] (numeric) = 0.4366222017597863 absolute error = 5.551115123125783e-17 relative error = 1.271377199957368e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.2154 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2154 Order of pole (three term test) = 1.865e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9199999999999999 y[1] (analytic) = 0.4589716365264023 y[1] (numeric) = 0.4589716365264022 absolute error = 1.110223024625157e-16 relative error = 2.418936021902284e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.2054 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2054 Order of pole (three term test) = 2.513e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9099999999999999 y[1] (analytic) = 0.4825766173484501 y[1] (numeric) = 0.4825766173484499 absolute error = 2.220446049250313e-16 relative error = 4.601230083319628e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.1954 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1954 Order of pole (three term test) = 4.047e-13 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = tan ( 2.0 * x + 3.0 ) ; Iterations = 10 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 110 %