##############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=(20.0);
glob_subiter_method=3;
glob_max_iter=1000;
glob_upper_ratio_limit=c(1.11);
glob_lower_ratio_limit=c(0.99);


/* 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                                 = 0.05                                         
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
 
TOP MAIN SOLVE Loop
x[1]                              = 1.05                                         
y[1] (closed_form)                = 1.502428952108273                            
y[1] (numeric)                    = 1.502428952108273                            
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   = 0.4316                                       
Order of pole (three term test)                    = 32.75                                        
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.05                                         
y[1] (closed_form)                = 2.461072691376713                            
y[1] (numeric)                    = 2.461072691376713                            
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   = 0.4091                                       
Order of pole (three term test)                    = 32.79                                        
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.05                                         
y[1] (closed_form)                = 2.995808324539061                            
y[1] (numeric)                    = 2.995808324539062                            
absolute error                    = 4.440892098500626e-16                        
relative error                    = 1.482368568818203e-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   = 0.09108                                      
Order of pole (three term test)                    = 32.01                                        
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.05                                         
y[1] (closed_form)                = 2.615002376525574                            
y[1] (numeric)                    = 2.615002376525575                            
absolute error                    = 4.440892098500626e-16                        
relative error                    = 1.698236352810135e-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   = 0.4849                                       
Order of pole (three term test)                    = 32.62                                        
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                  = 20 Minutes 0.0 Seconds
Percent Done                     = 121                                        %