##############ECHO OF PROBLEM#################
##############temp/sing2postode.ode#################
diff  (  y  ,  x  ,  1  )   =  1.0 /   ( x  *   x  +  1.0 )   ; 
!
/* BEGIN FIRST INPUT BLOCK */
Digits=16;
max_terms=20;
!
/* 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(1.0);

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=(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(arctan(c(x)));
}


/* END USER DEF BLOCK */
#######END OF ECHO OF PROBLEM#################
START of Soultion
 
TOP MAIN SOLVE Loop
x[1]                              = -2                                           
y[1] (closed_form)                = -1.10714871779409                            
y[1] (numeric)                    = -1.10714871779409                            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 14                                  
Correct digits                    = 16                                  
h                                 = 0.05                                         
Radius of convergence (given) for eq  1            = 2.236                                        
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     = 2.236                                        
Order of pole (six term test)                      = -1.155e-14                                   
 
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                    = 8                                   
Estimated correct digits          = 14                                  
Correct digits                    = 16                                  
h                                 = 0.05                                         
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)                      = -1.332e-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                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 16                                  
h                                 = 0.05                                         
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)                      = -6.661e-14                                   
 
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                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 16                                  
h                                 = 0.05                                         
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]                              = -1.6                                         
y[1] (closed_form)                = -1.012197011451334                           
y[1] (numeric)                    = -1.012197011451334                           
absolute error                    = 2.220446049250313e-16                        
relative error                    = 2.193689592173896e-14                      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 16                                  
h                                 = 0.05                                         
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)                      = 7.105e-15                                    
Finished!
diff  (  y  ,  x  ,  1  )   =  1.0 /   ( x  *   x  +  1.0 )   ; 
Iterations                       = 10                                  
Total Elapsed Time               = 0.0 Seconds
Elapsed Time(since restart)      = 0.0 Seconds
Time to Timeout                  = 20 Minutes 0.0 Seconds
Percent Done                     = 110                                        %