##############ECHO OF PROBLEM#################
##############temp/arccos_sqrtpostode.ode#################
diff ( y , x , 1 ) = arccos(sqrt(0.1 * x + 0.2));
!
/* BEGIN FIRST INPUT BLOCK */
Digits = 32;
max_terms = 30;
!
/* END FIRST INPUT BLOCK */
/* BEGIN SECOND INPUT BLOCK */
x_start = 0.1;
x_end = 0.5 ;
array_y_init[0 + 1] = exact_soln_y(x_start);
glob_h =    0.05;
glob_look_poles = true;
glob_max_iter = 1000000;
/* END SECOND INPUT BLOCK */
/* BEGIN OVERRIDE  BLOCK */
glob_h = 0.005 ;
glob_display_interval = 0.1;
glob_look_poles = true;
glob_max_iter = 10000;
glob_max_minutes = 10;
/* END OVERRIDE BLOCK */
!
/* BEGIN USER DEF BLOCK */
double exact_soln_y (double x) { 
return(10.0 * (0.1 * x + 0.2) * arccos(sqrt ( 0.1 * x + 0.2)) - 5.0 * sqrt( 0.1 * x +
0.2) * sqrt( 0.8 - 0.1 * x) + 5.0 * arcsin(sqrt( 0.1 * x + 0.2)));
}
/* END USER DEF BLOCK */
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1]                              = 0.1                                          
y[1] (analytic)                   = 2.642629173205489                            
y[1] (numeric)                    = 2.642629173205489                            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Correct digits                    = 16                                  
h                                 = 0.005                                        
 
TOP MAIN SOLVE Loop
NO POLE
x[1]                              = 0.2000000000000001                           
y[1] (analytic)                   = 2.751495138739343                            
y[1] (numeric)                    = 2.751495138739342                            
absolute error                    = 1.332267629550188e-15                        
relative error                    = 4.841977042927269e-14                      % 
Correct digits                    = 15                                  
h                                 = 0.005                                        
 
TOP MAIN SOLVE Loop
NO POLE
x[1]                              = 0.3000000000000002                           
y[1] (analytic)                   = 2.859153953861397                            
y[1] (numeric)                    = 2.859153953861395                            
absolute error                    = 2.220446049250313e-15                        
relative error                    = 7.766094743696874e-14                      % 
Correct digits                    = 15                                  
h                                 = 0.005                                        
 
TOP MAIN SOLVE Loop
NO POLE
x[1]                              = 0.4000000000000002                           
y[1] (analytic)                   = 2.965624522830128                            
y[1] (numeric)                    = 2.965624522830127                            
absolute error                    = 1.332267629550188e-15                        
relative error                    = 4.492367861453985e-14                      % 
Correct digits                    = 15                                  
h                                 = 0.005                                        
 
TOP MAIN SOLVE Loop
NO POLE
x[1]                              = 0.5000000000000003                           
y[1] (analytic)                   = 3.070924246521893                            
y[1] (numeric)                    = 3.070924246521889                            
absolute error                    = 4.440892098500626e-15                        
relative error                    = 1.446109295444311e-13                      % 
Correct digits                    = 14                                  
h                                 = 0.005                                        
Finished!
diff ( y , x , 1 ) = arccos(sqrt(0.1 * x + 0.2));
Iterations                        = 80                                  
Total Elapsed Time               = 4 Seconds
Elapsed Time(since restart)      = 4 Seconds
Time to Timeout                  = 9 Minutes 56 Seconds
Percent Done                     = 101.3                                      %