1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
|
#Solving initial value problem using 4th order Runge-Kutta method.
'''
Solving initial value problem using 4th order Runge-Kutta method.
Sine function is calculated using its derivative, cosine.
'''
import math
def rk4(x, y, yprime, dx = 0.01): # x, y , derivative, stepsize
k1 = dx * yprime(x)
k2 = dx * yprime(x + dx/2.0)
k3 = dx * yprime(x + dx/2.0)
k4 = dx * yprime(x + dx)
return y + ( k1/6 + k2/3 + k3/3 + k4/6 )
h = 0.01 # stepsize
x = 0.0 # initail values
y = 0.0
while x < math.pi:
print x, y, math.sin(x)
y = rk4(x,y,math.cos) # Runge-Kutta method
x = x + h
|
