How to Optimize a 2D Nonlinear Heat Conduction Solver in MATLAB?

[range.rover]

Hi friends,

i have developed an code for a non linear heat conduction in 2 dimensions with dirichlet boundary condition by finite difference method in Matlab. my code is running slow to give output.
If anybody has any idea of solving this equation or have written any Code for this equation, please share it with me.
Any body who has worked on this can share the idea with me.

(d²t/dx² + d²t/dy²)(K(t)) = Q
K(t)= (a - b*t) ; a>>b.

 

[Chestermiller]

If K represents the thermal conductivity, then this formulation is incorrect. It should read:
$$\frac{\partial}{\partial x}\left(K(T)\frac{\partial T}{\partial x}\right)+\frac{\partial}{\partial y}\left(K(T)\frac{\partial T}{\partial y}\right)=Q$$
Chet