Hello,

it is

$\displaystyle \frac{\partial u}{\partial t} = k*\frac{\partial^2 u}{\partial x^2}$ (as known as heat equation)

Show that

$\displaystyle \frac{\partial^2 u}{\partial x^2} \approx \frac{u(t,x_{i+1})-2u(t,x_i) + u(t,x_{i-1})}{h^2} $

Anyone knows how to show this?

Best Regards,

Rapha