Runge kutta methord

what is Runge kutta methord

def dydx(x,y):

return (x+y)/2

pass

def rk(x0,y0,x,h):

n=round((x0-x)/h)

k1=0

k2=0

k3=0

k4=0

y=y0

for t in range(1,n-1):

k1=h*dydx(x0,y0)

k2=h*dydx(x0+h/2,y0+k1/2)

k3=h*dydx(x0+h/2,y0+k2/2)

k4=h*dydx(x0+h,y0+k3)

x0=x0+h

num=y+(h*(k1+2*(k2+k3)+k4)/6)

return num

# Finds value of y for a given x  

# using step size h  

# and initial value y0 at x0. 

x0 = 0

y = 1  

x = 2

h = 0.2

print("x=",x,"y=",y,"x0=",x0,"h=",h)

print("the function is dy/dx=(x+y)/2")

print(rk(x0,y,x,h))