##############ECHO OF PROBLEM################# ##############temp/sing2_backpostode.ode################# diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; ! // 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_type_given_pole=2; array_given_rad_poles[1][1]=0.0; array_given_rad_poles[1][2]=1.0; 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=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(arctan(x)); } // 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 = 0.9827937232473291 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 = 8.40342006704583e-104 estimated_step_error = 8.40342006704583e-104 Double H and LOOP opt_iter = 2 min_size = 0.9827937232473291 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 = 5.507311820934126e-99 estimated_step_error = 5.507311820934126e-99 Double H and LOOP opt_iter = 3 min_size = 0.9827937232473291 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 = 3.609332752318682e-94 estimated_step_error = 3.609332752318682e-94 Double H and LOOP opt_iter = 4 min_size = 0.9827937232473291 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 = 2.36549210550889e-89 estimated_step_error = 2.36549210550889e-89 Double H and LOOP opt_iter = 5 min_size = 0.9827937232473291 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 = 1.550353491923595e-84 estimated_step_error = 1.550353491923595e-84 Double H and LOOP opt_iter = 6 min_size = 0.9827937232473291 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 = 1.016176745519009e-79 estimated_step_error = 1.016176745519009e-79 Double H and LOOP opt_iter = 7 min_size = 0.9827937232473291 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 = 6.661412629905312e-75 estimated_step_error = 6.661412629905312e-75 Double H and LOOP opt_iter = 8 min_size = 0.9827937232473291 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 = 4.367978265106604e-70 estimated_step_error = 4.367978265106604e-70 Double H and LOOP opt_iter = 9 min_size = 0.9827937232473291 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 = 2.865684566221823e-65 estimated_step_error = 2.865684566221823e-65 Double H and LOOP opt_iter = 10 min_size = 0.9827937232473291 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 = 1.882099662642142e-60 estimated_step_error = 1.882099662642142e-60 Double H and LOOP opt_iter = 11 min_size = 0.9827937232473291 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 = 1.238752398765103e-55 estimated_step_error = 1.238752398765103e-55 Double H and LOOP opt_iter = 12 min_size = 0.9827937232473291 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 = 8.187702806745811e-51 estimated_step_error = 8.187702806745811e-51 Double H and LOOP opt_iter = 13 min_size = 0.9827937232473291 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 = 5.456752634924327e-46 estimated_step_error = 5.456752634924327e-46 Double H and LOOP opt_iter = 14 min_size = 0.9827937232473291 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 = 3.694904616149563e-41 estimated_step_error = 3.694904616149563e-41 Double H and LOOP opt_iter = 15 min_size = 0.9827937232473291 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 = 2.57631618160252e-36 estimated_step_error = 2.57631618160252e-36 Double H and LOOP opt_iter = 16 min_size = 0.9827937232473291 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 = 1.889142408263728e-31 estimated_step_error = 1.889142408263728e-31 Double H and LOOP opt_iter = 17 min_size = 0.9827937232473291 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 = 1.495487843488867e-26 estimated_step_error = 1.495487843488867e-26 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) = -1.012197011451334 y[1] (numeric) = -1.012197011451334 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = -0.1 Radius of convergence (given) for eq 1 = 1.887 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.887 Order of pole (six term test) = 3.553e-15 TOP MAIN SOLVE Loop x[1] = -1.7 y[1] (closed_form) = -1.039072259536091 y[1] (numeric) = -1.039072259536091 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = -0.1 Radius of convergence (given) for eq 1 = 1.972 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.972 Order of pole (six term test) = 1.155e-14 TOP MAIN SOLVE Loop x[1] = -1.8 y[1] (closed_form) = -1.06369782240256 y[1] (numeric) = -1.06369782240256 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = -0.1 Radius of convergence (given) for eq 1 = 2.059 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.059 Order of pole (six term test) = 4.441e-15 TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (closed_form) = -1.086318397757873 y[1] (numeric) = -1.086318397757873 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = -0.1 Radius of convergence (given) for eq 1 = 2.147 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.147 Order of pole (six term test) = -5.24e-14 Finished! diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; 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 %