##############ECHO OF PROBLEM#################
##############temp/sing7postode.ode#################
diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ;
!
/* BEGIN FIRST INPUT BLOCK */
Digits=64;
max_terms=20;
!
/* END FIRST INPUT BLOCK */
/* BEGIN SECOND INPUT BLOCK */
x_start=c(2.0);
x_end=c(3.0);
array_y_init[0 + 1] = exact_soln_y(x_start);
glob_look_poles=true;
glob_type_given_pole=1;
array_given_rad_poles[1][1]=c(6.0);
/* 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(6.0) ) / ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )) ;
}
/* 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 = 1e-06
estimated_answer = 1
desired_abs_gbl_error = 1e-08
range = 1
estimated_steps = 1000000
step_error = 5.000000000000001e-13
est_needed_step_err = 5.000000000000001e-13
opt_iter = 1
SETTING H FOR MIN H
Radius of convergence (given) for eq 1 = 4
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 4.286
Order of pole (ratio test) = 1
Radius of convergence (three term test) for eq 1 = 4
Order of pole (three term test) = 5.332e-14
NO COMPLEX POLE (six term test) for Equation 1
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (closed_form) = -0.0009765625
y[1] (numeric) = -0.0009765625
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 = 4
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 4.286
Order of pole (ratio test) = 1
Radius of convergence (three term test) for eq 1 = 4
Order of pole (three term test) = 5.914e-14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (closed_form) = -0.001108350100176561
y[1] (numeric) = -0.001108350099311493
absolute error = 8.650673493509897e-13
relative error = 7.805000867624625e-08 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 10
h = 0.05
Radius of convergence (given) for eq 1 = 3.9
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 4.179
Order of pole (ratio test) = 1
Radius of convergence (three term test) for eq 1 = 3.9
Order of pole (three term test) = 2.377e-14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.199999999999999
y[1] (closed_form) = -0.001262065854394351
y[1] (numeric) = -0.001262065852383357
absolute error = 2.010993151516094e-12
relative error = 1.593413802072273e-07 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 9
h = 0.05
Radius of convergence (given) for eq 1 = 3.8
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 4.071
Order of pole (ratio test) = 1
Radius of convergence (three term test) for eq 1 = 3.8
Order of pole (three term test) = 3.732e-14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.299999999999999
y[1] (closed_form) = -0.001442086727182296
y[1] (numeric) = -0.00144208672364209
absolute error = 3.54020545517697e-12
relative error = 2.454918548549576e-07 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 9
h = 0.05
Radius of convergence (given) for eq 1 = 3.7
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 3.964
Order of pole (ratio test) = 1
Radius of convergence (three term test) for eq 1 = 3.7
Order of pole (three term test) = 5.716e-14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.399999999999999
y[1] (closed_form) = -0.001653817168792017
y[1] (numeric) = -0.001653817163195177
absolute error = 5.596839831867317e-12
relative error = 3.384195023175002e-07 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 9
h = 0.05
Radius of convergence (given) for eq 1 = 3.6
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 3.857
Order of pole (ratio test) = 1
Radius of convergence (three term test) for eq 1 = 3.6
Order of pole (three term test) = 4.263e-14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.499999999999998
y[1] (closed_form) = -0.001903968584518351
y[1] (numeric) = -0.001903968576132751
absolute error = 8.38559950644413e-12
relative error = 4.404274090775214e-07 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 9
h = 0.05
Radius of convergence (given) for eq 1 = 3.5
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 3.75
Order of pole (ratio test) = 1
Radius of convergence (three term test) for eq 1 = 3.5
Order of pole (three term test) = 6.185e-14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.599999999999998
y[1] (closed_form) = -0.002200925867886689
y[1] (numeric) = -0.002200925855686626
absolute error = 1.220006344213043e-11
relative error = 5.54315055320097e-07 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 9
h = 0.05
Radius of convergence (given) for eq 1 = 3.4
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 3.643
Order of pole (ratio test) = 1
Radius of convergence (three term test) for eq 1 = 3.4
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.699999999999998
y[1] (closed_form) = -0.002555231782136432
y[1] (numeric) = -0.002555231764670798
absolute error = 1.746563354013131e-11
relative error = 6.835244325870225e-07 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 9
h = 0.05
Radius of convergence (given) for eq 1 = 3.3
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 3.536
Order of pole (ratio test) = 1
Radius of convergence (three term test) for eq 1 = 3.3
Order of pole (three term test) = 2.975e-14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.799999999999997
y[1] (closed_form) = -0.002980232238769518
y[1] (numeric) = -0.00298023221396402
absolute error = 2.480549793348885e-11
relative error = 8.323343936353958e-07 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 9
h = 0.05
Radius of convergence (given) for eq 1 = 3.2
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 3.429
Order of pole (ratio test) = 1
Radius of convergence (three term test) for eq 1 = 3.2
Order of pole (three term test) = 3.93e-14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.899999999999997
y[1] (closed_form) = -0.003492943259127715
y[1] (numeric) = -0.003492943223984484
absolute error = 3.514323077338788e-11
relative error = 1.006120860439174e-06 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 8
h = 0.05
Radius of convergence (given) for eq 1 = 3.1
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 3.321
Order of pole (ratio test) = 1
Radius of convergence (three term test) for eq 1 = 3.1
Order of pole (three term test) = 5.013e-14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.999999999999996
y[1] (closed_form) = -0.004115226337448535
y[1] (numeric) = -0.004115226287583987
absolute error = 4.986454738703516e-11
relative error = 1.211708501504962e-06 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 8
h = 0.05
Radius of convergence (given) for eq 1 = 3
Order of pole (given) = 0
Radius of convergence (ratio test) for eq 1 = 3.214
Order of pole (ratio test) = 1
Radius of convergence (three term test) for eq 1 = 3
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ;
Iterations = 21
Total Elapsed Time = 0.0 Seconds
Elapsed Time(since restart) = 0.0 Seconds
Time to Timeout = 5 Minutes 0.0 Seconds
Percent Done = 110 %