##############ECHO OF PROBLEM################# ##############temp/sing1_backpostode.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=-1.5; x_end=-2.0; 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 min_size = 0.444444246913668 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 = 1.15025757751079e-98 estimated_step_error = 1.15025757751079e-98 Double H and LOOP opt_iter = 2 min_size = 0.444444246913668 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 = 7.538325399397697e-94 estimated_step_error = 7.538325399397697e-94 Double H and LOOP opt_iter = 3 min_size = 0.444444246913668 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 = 4.940313446481449e-89 estimated_step_error = 4.940313446481449e-89 Double H and LOOP opt_iter = 4 min_size = 0.444444246913668 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 = 3.237679249464048e-84 estimated_step_error = 3.237679249464048e-84 Double H and LOOP opt_iter = 5 min_size = 0.444444246913668 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 = 2.121839481886198e-79 estimated_step_error = 2.121839481886198e-79 Double H and LOOP opt_iter = 6 min_size = 0.444444246913668 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 = 1.390560870335943e-74 estimated_step_error = 1.390560870335943e-74 Double H and LOOP opt_iter = 7 min_size = 0.444444246913668 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 = 9.113076797113529e-70 estimated_step_error = 9.113076797113529e-70 Double H and LOOP opt_iter = 8 min_size = 0.444444246913668 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 = 5.972211111445129e-65 estimated_step_error = 5.972211111445129e-65 Double H and LOOP opt_iter = 9 min_size = 0.444444246913668 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 = 3.913771472025888e-60 estimated_step_error = 3.913771472025888e-60 Double H and LOOP opt_iter = 10 min_size = 0.444444246913668 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 = 2.564697565332385e-55 estimated_step_error = 2.564697565332385e-55 Double H and LOOP opt_iter = 11 min_size = 0.444444246913668 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 = 1.680496576012369e-50 estimated_step_error = 1.680496576012369e-50 Double H and LOOP opt_iter = 12 min_size = 0.444444246913668 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 = 1.10093248964071e-45 estimated_step_error = 1.10093248964071e-45 Double H and LOOP opt_iter = 13 min_size = 0.444444246913668 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 = 7.209863449232822e-41 estimated_step_error = 7.209863449232822e-41 Double H and LOOP opt_iter = 14 min_size = 0.444444246913668 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 = 4.718244967515527e-36 estimated_step_error = 4.718244967515527e-36 Double H and LOOP opt_iter = 15 min_size = 0.444444246913668 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 = 3.083259896597151e-31 estimated_step_error = 3.083259896597151e-31 Double H and LOOP opt_iter = 16 min_size = 0.444444246913668 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 = 2.009093628178445e-26 estimated_step_error = 2.009093628178445e-26 Double H and LOOP opt_iter = 17 min_size = 0.444444246913668 min_size = 1 glob_desired_digits_correct = 16 estimated_h = -0.065536 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = -0.5 estimated_steps = 7.62939453125 step_error = 1.810193359837562e-18 est_needed_step_err = 1.810193359837562e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.301794390555977e-21 estimated_step_error = 1.301794390555977e-21 Double H and LOOP opt_iter = 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL START of Soultion TOP MAIN SOLVE Loop x[1] = -1.6 y[1] (closed_form) = 0.3906248474121689 y[1] (numeric) = 0.390624847412169 absolute error = 5.551115123125783e-17 relative error = 1.421086026631713e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = -0.1 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] = -1.7 y[1] (closed_form) = 0.3460206415153489 y[1] (numeric) = 0.3460206415153489 absolute error = 5.551115123125783e-17 relative error = 1.604272825694864e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = -0.1 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] = -1.8 y[1] (closed_form) = 0.3086418800488023 y[1] (numeric) = 0.3086418800488024 absolute error = 1.110223024625157e-16 relative error = 3.597123710008533e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = -0.1 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] = -1.9 y[1] (closed_form) = 0.2770082335157247 y[1] (numeric) = 0.2770082335157248 absolute error = 1.110223024625157e-16 relative error = 4.007906229119841e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = -0.1 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 Finished! diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; Iterations = 5 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 = 3 Minutes 0.0 Seconds Percent Done = 0 %