I am trying to model the process of laser ablation on a material using MATLAB. The governing equation is of the form:
∂T(x,t)/∂t = ∂/∂x(A*∂T/∂x) + B*exp(-C*t2)*exp(-D*x)
with one Initial condition and two boundary conditions.
Using the built-in 'pdepe' function in Matlab gave inaccurate results, so I have been reading material on solving it numerically. This being a non-linear parabolic pde (correct me if wrong), I am facing difficulty on how to proceed. All the materials that I have referred to so far only address problems where the last term (source term) of the equation is a function of T(x,t). Please guide me.