PDE problem on two variable(x&t), looking for expample code?

Hello to all,

Thank you for your kind help and support!

I have to solve a system of 3 partial differential equations. The fully implicit finite difference method is applied for approximation. The first part of the solution with MatLab is to obtain the unknowing variables for every point of the spatial co-ordinate, x. I’ve already composed a rough code for this.

And now I have to extend this with an outer loop, which gives a solution for the different time levels. One of the problems here is that I need the values for the examined variables from the previous time level.

Any example code for the similar problems is highly appreciated!

Thank you in advance!