I posted this problem already but I had no reply , sorry for the repitition.

I'm trying to program a simulation of the Viscous Burger's Equation in 1 dimension. I'm going to use an implicit finite difference scheme (Crank-Nicolson) to do this.

The problem I have is the fact that the Burger's equation I mentioned is non-linear, I need to have this equation in conservation form before I apply my scheme. The Burgers equation in conservation form is as follows:

Where F is a flux function .
and v is the viscosity which is a constant.

(note: I didn't know how to show these as partial derivatives. All derivatives are partial here.)

I was just wondering how I would go about linearizing this equation

I want to thank you for any help you can give in advance.

All the best,