solvinf stiff equation using ode23s for a multivariable problem

Hi, I am solving a set of coupled differential equation very similar to the heat equation. The equation depends on position as well as time and the problem is stiff. I ve been trying to find something online but no hope. I found only one example which converted the continuum space to discreet set of point but it didnt work well in my case. Is there any where documentation how to use ode23s for a similar problem time-space dependent?

I appreciate any help. Thanks