Numerical Analysis and SImulation

Dear Friends i am working on the following topic:
'Prediction of tool and chip temperature in continuous and interrupted machining'
using the finite difference method now i have the partial differential equation for chip temperature model

now to determine the temperature distribution within the chip due to shearing along the cut, we can use the above equation whiich can be written in the following form also
[A].{Tc } = {C}
where
[A] is the square coefficient matrix
{Tc} is the chip temperature array
and
{C} is the heat generation array

now i think matlab is most suitable software to simulate the results because it is a matrix based language.
But how to determine the coefficient matrix from the above partial differential equation ?
Is there any way to simulate this cutting process in MATLAB?
Does ANSYS works?(for simulation)
Any idea???//
I need your immediate assistance friends and professors.
with best regards
Ammar Aziz