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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*t^{2})*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.

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# Suggestions for scheme to use to solve PDE numerically

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