Use a forward difference for the time derivative and a central difference for the spatial derivative:
(\frac{V_{x,t+1}\,-\,V_{x,t}}{\delta t}=\(0.16+0.08\sin (t))\frac{V_{x+1,t},-,2V_{x,t},+,V_{x-1,t}}{(\delta x)^2})
Solve for (V_{x,t+1}=...) and Bob's your uncle.