# Numerical Solution of a Backward Parabolic PDE using finite difference?

I have a PDE of the form $$\frac{\partial u}{\partial t} + \frac{\partial }{\partial x} \bigg( A(u) \frac{\partial u}{\partial x} \bigg) + \big( other \hspace{0.2cm} terms \big)= 0$$. I read on wiki that this is a backward parabolic PDE. I need some help to resolve the second term using finite differences. I've managed to discretize the other non-linear terms in my equations and obtain a stable evolution save for this one. Thank you for your input!