##############ECHO OF PROBLEM#################
##############temp/sin_lg_hpostode.ode#################
diff  (  y  ,  x  ,  1  )   =  sin  (  x  )   ; 
!
// BEGIN FIRST INPUT BLOCK

Digits=16;
max_terms=40;

!
// END FIRST INPUT BLOCK
// BEGIN SECOND INPUT BLOCK

x_start=c(0.0);
x_end=c(5.0);
array_y_init[0 + 1] = exact_soln_y(x_start);
glob_look_poles=false;
glob_max_h=c(1.0);
glob_min_h=c(1.0);
glob_display_interval=c(1.0);








glob_type_given_pole=3;

// END SECOND INPUT BLOCK
// BEGIN OVERRIDE  BLOCK
glob_desired_digits_correct=8;
glob_max_minutes=(3.0);
glob_subiter_method=3;
glob_max_iter=100000;
glob_upper_ratio_limit=c(1.000001);
glob_lower_ratio_limit=c(0.999999);
glob_look_poles=true;
glob_h=c(0.001);
glob_display_interval=c(0.01);
// END OVERRIDE BLOCK
!
// BEGIN USER DEF BLOCK

double exact_soln_y (double x) { 

return(c(2.0) - cos(c(x)));

}
// END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
 
TOP MAIN SOLVE Loop
x[1]                              = 0                                            
y[1] (closed_form)                = 1                                            
y[1] (numeric)                    = 1                                            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 14                                  
Correct digits                    = 16                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
SETTING H FOR MIN H
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.001                                        
Order of pole (three term test)                    = 32                                           
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.001                                        
y[1] (closed_form)                = 1.460539435127553                            
y[1] (numeric)                    = 1.460539435127553                            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 16                                  
h                                 = 1                                            
SETTING H FOR POLE
SETTING H FOR MIN H
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4542                                       
Order of pole (three term test)                    = 32.71                                        
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.001                                        
y[1] (closed_form)                = 2.417055925749017                            
y[1] (numeric)                    = 2.417055925749017                            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 16                                  
h                                 = 1                                            
SETTING H FOR POLE
SETTING H FOR MIN H
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3791                                       
Order of pole (three term test)                    = 32.83                                        
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.001                                        
y[1] (closed_form)                = 2.990133121588778                            
y[1] (numeric)                    = 2.990133121588778                            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 16                                  
h                                 = 1                                            
SETTING H FOR POLE
SETTING H FOR MIN H
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1387                                       
Order of pole (three term test)                    = 32.02                                        
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.000999999999999                            
y[1] (closed_form)                = 2.652886491672655                            
y[1] (numeric)                    = 2.652886491672655                            
absolute error                    = 4.440892098500626e-16                        
relative error                    = 1.67398496409118e-14                       % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 16                                  
h                                 = 1                                            
SETTING H FOR POLE
SETTING H FOR MIN H
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4945                                       
Order of pole (three term test)                    = 32.57                                        
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff  (  y  ,  x  ,  1  )   =  sin  (  x  )   ; 
Iterations                       = 6                                   
Total Elapsed Time               = 0.0 Seconds
Elapsed Time(since restart)      = 0.0 Seconds
Time to Timeout                  = 3 Minutes 0.0 Seconds
Percent Done                     = 120                                        %