from sympy import * 
var('x y') 
f=lambda x,y:(x**2+(y/2)) 
x0=1 
y0=2 
y1=2.2156 
y2=2.4649 
y3=2.7514 
h=0.1 
x1=x0+h 
x2=x1+h 
x3=x2+h 
x4=x3+h 
y10 =f (x0,y0 ) 
y11 =f ( x1 , y1 ) 
y12 =f ( x2 , y2 ) 
y13 =f ( x3 , y3 ) 
y4p =y0+( 4*h/3 )*( 2*y11-y12+2*y13 ) 
print ('predicted value of y4 is %3.3f '%y4p ) 
y14 =f ( x4 , y4p ) ; 
for i in range (1 , 4 ): 
 y4=y2+( h/3 )*( y14 +4*y13 +y12 ) ; 
 print ('corrected value of y4 after \t iteration %d is \t 
%3.5f\t '% (i , y4 ) ) 
 y14=f (x4 , y4 );