##############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=30;
!
/* END FIRST INPUT BLOCK */
/* BEGIN SECOND INPUT BLOCK */
x_start=c(-2.0);
x_end=c(-1.5);
array_y_init[0 + 1] = exact_soln_y(x_start);
glob_look_poles=true;
glob_max_h=c(0.001);
glob_min_h=c(0.001);
glob_type_given_pole=2;
array_given_rad_poles[1][1]=c(0.0);
array_given_rad_poles[1][2]=c(0.001);
array_given_ord_poles[1][1]=c(1.0);
array_given_ord_poles[1][2]=c(0.0);
/* END SECOND INPUT BLOCK */
/* BEGIN OVERRIDE BLOCK */
glob_desired_digits_correct=8;
glob_max_minutes=(5.0);
glob_subiter_method=3;
glob_max_iter=1000;
glob_upper_ratio_limit=c(1.1);
glob_lower_ratio_limit=c(0.9);
/* END OVERRIDE BLOCK */
!
/* BEGIN USER DEF BLOCK */
double exact_soln_y (double x) {
return(c(1.0) / (c(x) * c(x) + c(0.000001))) ;
}
/* END USER DEF BLOCK */
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
glob_desired_digits_correct = 8
estimated_h = 0.001
estimated_answer = 1
desired_abs_gbl_error = 1e-08
range = 0.5
estimated_steps = 500
step_error = 1.49071198499986e-11
est_needed_step_err = 1.49071198499986e-11
opt_iter = 1
SETTING H FOR MIN H
SETTING H FOR DISPLAY INTERVAL
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 = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.05
Radius of convergence (given) for eq 1 = 2
Order of pole (given) = 1
Radius of convergence (ratio test) for eq 1 = 1.923
Order of pole (ratio test) = 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 = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.05
Radius of convergence (given) for eq 1 = 1.95
Order of pole (given) = 1
Radius of convergence (ratio test) for eq 1 = 1.875
Order of pole (ratio test) = 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 = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.05
Radius of convergence (given) for eq 1 = 1.9
Order of pole (given) = 1
Radius of convergence (ratio test) for eq 1 = 1.827
Order of pole (ratio test) = 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 = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.05
Radius of convergence (given) for eq 1 = 1.85
Order of pole (given) = 1
Radius of convergence (ratio test) for eq 1 = 1.779
Order of pole (ratio test) = 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 = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.05
Radius of convergence (given) for eq 1 = 1.8
Order of pole (given) = 1
Radius of convergence (ratio test) for eq 1 = 1.731
Order of pole (ratio test) = 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 = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.05
Radius of convergence (given) for eq 1 = 1.75
Order of pole (given) = 1
Radius of convergence (ratio test) for eq 1 = 1.683
Order of pole (ratio test) = 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 = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.05
Radius of convergence (given) for eq 1 = 1.7
Order of pole (given) = 1
Radius of convergence (ratio test) for eq 1 = 1.635
Order of pole (ratio test) = 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 = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.05
Radius of convergence (given) for eq 1 = 1.65
Order of pole (given) = 1
Radius of convergence (ratio test) for eq 1 = 1.587
Order of pole (ratio test) = 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 = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.05
Radius of convergence (given) for eq 1 = 1.6
Order of pole (given) = 1
Radius of convergence (ratio test) for eq 1 = 1.538
Order of pole (ratio test) = 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 = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.05
Radius of convergence (given) for eq 1 = 1.55
Order of pole (given) = 1
Radius of convergence (ratio test) for eq 1 = 1.49
Order of pole (ratio test) = 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 = 5 Minutes 0.0 Seconds
Percent Done = 110 %