##############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_h=0.1; glob_type_given_pole=2; 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=16; glob_max_minutes=3.0; glob_subiter_method=3; glob_max_iter=100000000; // 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 = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.5 estimated_steps = 500000 step_error = 7.071067811865475e-21 est_needed_step_err = 7.071067811865475e-21 opt_iter = 1 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 min_size = 0.2499999375000156 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.5 estimated_steps = 500000 step_error = 7.071067811865475e-21 est_needed_step_err = 7.071067811865475e-21 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 Double H and LOOP opt_iter = 2 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 min_size = 0.2499999375000156 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.5 estimated_steps = 250000 step_error = 9.999999999999999e-21 est_needed_step_err = 9.999999999999999e-21 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 Double H and LOOP opt_iter = 3 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 min_size = 0.2499999375000156 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.5 estimated_steps = 125000 step_error = 1.414213562373095e-20 est_needed_step_err = 1.414213562373095e-20 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 Double H and LOOP opt_iter = 4 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 min_size = 0.2499999375000156 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.5 estimated_steps = 62500 step_error = 2e-20 est_needed_step_err = 2e-20 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 Double H and LOOP opt_iter = 5 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 min_size = 0.2499999375000156 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.5 estimated_steps = 31250 step_error = 2.82842712474619e-20 est_needed_step_err = 2.82842712474619e-20 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 Double H and LOOP opt_iter = 6 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 min_size = 0.2499999375000156 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.5 estimated_steps = 15625 step_error = 4e-20 est_needed_step_err = 4e-20 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 Double H and LOOP opt_iter = 7 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 min_size = 0.2499999375000156 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.5 estimated_steps = 7812.5 step_error = 5.65685424949238e-20 est_needed_step_err = 5.65685424949238e-20 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 Double H and LOOP opt_iter = 8 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 min_size = 0.2499999375000156 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.5 estimated_steps = 3906.25 step_error = 8e-20 est_needed_step_err = 8e-20 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 Double H and LOOP opt_iter = 9 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 min_size = 0.2499999375000156 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.5 estimated_steps = 1953.125 step_error = 1.131370849898476e-19 est_needed_step_err = 1.131370849898476e-19 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 Double H and LOOP opt_iter = 10 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 min_size = 0.2499999375000156 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.5 estimated_steps = 976.5625 step_error = 1.6e-19 est_needed_step_err = 1.6e-19 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 Double H and LOOP opt_iter = 11 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 min_size = 0.2499999375000156 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.5 estimated_steps = 488.28125 step_error = 2.262741699796952e-19 est_needed_step_err = 2.262741699796952e-19 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 Double H and LOOP opt_iter = 12 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 min_size = 0.2499999375000156 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.5 estimated_steps = 244.140625 step_error = 3.2e-19 est_needed_step_err = 3.2e-19 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 Double H and LOOP opt_iter = 13 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 min_size = 0.2499999375000156 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.5 estimated_steps = 122.0703125 step_error = 4.525483399593904e-19 est_needed_step_err = 4.525483399593904e-19 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 Double H and LOOP opt_iter = 14 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 min_size = 0.2499999375000156 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.5 estimated_steps = 61.03515625 step_error = 6.4e-19 est_needed_step_err = 6.4e-19 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 Double H and LOOP opt_iter = 15 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 min_size = 0.2499999375000156 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.5 estimated_steps = 30.517578125 step_error = 9.050966799187808e-19 est_needed_step_err = 9.050966799187808e-19 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 Double H and LOOP opt_iter = 16 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 min_size = 0.2499999375000156 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.5 estimated_steps = 15.2587890625 step_error = 1.28e-18 est_needed_step_err = 1.28e-18 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 Double H and LOOP opt_iter = 17 SETTING H FOR DISPLAY INTERVAL 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 = 1.526 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.526 Order of pole (six term test) = 1 START of Soultion TOP MAIN SOLVE Loop x[1] = -2 y[1] (closed_form) = 0.2499999375000156 y[1] (numeric) = 0.2499999375000156 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.05 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] = -1.95 y[1] (closed_form) = 0.2629848092084657 y[1] (numeric) = 0.2629848092084657 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.05 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] = -1.9 y[1] (closed_form) = 0.2770082335157248 y[1] (numeric) = 0.2770082335157248 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05 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] = -1.85 y[1] (closed_form) = 0.2921839905963505 y[1] (numeric) = 0.2921839905963505 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05 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] = -1.8 y[1] (closed_form) = 0.3086418800488025 y[1] (numeric) = 0.3086418800488025 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05 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] = -1.75 y[1] (closed_form) = 0.3265305056226921 y[1] (numeric) = 0.3265305056226921 absolute error = 5.551115123125783e-17 relative error = 1.700029561568783e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05 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] = -1.7 y[1] (closed_form) = 0.3460206415153491 y[1] (numeric) = 0.346020641515349 absolute error = 5.551115123125783e-17 relative error = 1.604272825694863e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05 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] = -1.65 y[1] (closed_form) = 0.3673093233023607 y[1] (numeric) = 0.3673093233023607 absolute error = 5.551115123125783e-17 relative error = 1.511291647382506e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05 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] = -1.6 y[1] (closed_form) = 0.3906248474121691 y[1] (numeric) = 0.3906248474121691 absolute error = 5.551115123125783e-17 relative error = 1.421086026631712e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05 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] = -1.55 y[1] (closed_form) = 0.4162329172807838 y[1] (numeric) = 0.4162329172807838 absolute error = 5.551115123125783e-17 relative error = 1.333655963442481e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05 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 Finished! diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; Iterations = 10 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 110 %