##############ECHO OF PROBLEM#################
##############temp/cos_sqrt_linpostode.ode#################
diff  (  y  ,  x  ,  1  )   =  cos ( sqrt ( 2.0 * x  +  3.0 )  )  ; 
!
/* BEGIN FIRST INPUT BLOCK */
Digits=32;
max_terms=30;
!
/* END FIRST INPUT BLOCK */
/* BEGIN SECOND INPUT BLOCK */
x_start=c(-1.4);
x_end=c(-1.3);
array_y_init[0 + 1] = exact_soln_y(x_start);
glob_look_poles=true;
glob_max_h=0.0001;
glob_upper_ratio_limit=c(1.001);
glob_lower_ratio_limit=c(0.999);









glob_type_given_pole=1;

array_given_rad_poles[1][1]=c(-1.5);

array_given_rad_poles[1][2]=c(0.0);

array_given_ord_poles[1][1]=c(0.5);

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(cos(sqrt(c(2.0)*c(x)+c(3.0)))+sqrt(c(2.0)*c(x)+c(3.0))*sin(sqrt(c(2.0)*c(x)+c(3.0))));
}
/* END USER DEF BLOCK */
#######END OF ECHO OF PROBLEM#################
START of Soultion
 
TOP MAIN SOLVE Loop
x[1]                              = -1.4                                         
y[1] (closed_form)                = 1.095055278569961                            
y[1] (numeric)                    = 1.095055278569961                            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 16                                  
h                                 = 0.05                                         
SETTING H FOR POLE
Radius of convergence (given) for eq  1            = 0.1                                          
Order of pole (given)                              = 0.5                                          
Radius of convergence (ratio test) for eq  1       = 0.1114                                       
Order of pole (ratio test)                         = 1                                            
Radius of convergence (three term test) for eq 1   = 0.09967                                      
Order of pole (three term test)                    = 1.64                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = -1.300328912053475                           
y[1] (closed_form)                = 1.18017468138312                             
y[1] (numeric)                    = 1.180652748830341                            
absolute error                    = 0.0004780674472206758                        
relative error                    = 0.0405081938091062                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.00996710879465252                          
Radius of convergence (given) for eq  1            = 0.1997                                       
Order of pole (given)                              = 0.5                                          
Radius of convergence (ratio test) for eq  1       = 0.2225                                       
Order of pole (ratio test)                         = 1                                            
Radius of convergence (three term test) for eq 1   = 0.199                                        
Order of pole (three term test)                    = 1.642                                        
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff  (  y  ,  x  ,  1  )   =  cos ( sqrt ( 2.0 * x  +  3.0 )  )  ; 
Iterations                       = 11                                  
Total Elapsed Time               = 0.0 Seconds
Elapsed Time(since restart)      = 0.0 Seconds
Time to Timeout                  = 20 Minutes 0.0 Seconds
Percent Done                     = 119.6                                      %