$$ \frac {\partial^2 C}{dt^2} = c^2 \frac {\partial^2 C}{dx^2} $$

$$\frac {C^{t+1}_{x} - 2C^{t}_{x} + C^{t-1}_{x}}{\Delta t^2} = c^2 \frac {C^{t}_{x+1} - 2C^{t}_{x} + C^{t}_{x-1}}{\Delta x^2}$$

if $ \alpha = \frac {c \Delta t}{\Delta x} $

$$ C^{t+1}_{x} = \alpha^2 C^{t}_{x+1} + 2(1 - \alpha^2)C^{t}_{x} + \alpha^2 C^{t}_{x-1} - C^{t-1}_{x}$$



In [ ]:

    
L = 1
nx = 100
dx = L/(nx+1)

T = 100
dt = 0.5*dx
nx = (T/(dt))-1

C = zeros()