Journal article
Semiimplicit finitedifference method with predictorcorrector algorithm for solution of diffusion equation with nonlinear terms
Publication Details
Authors:  Lipp, V.; Rethfeld, B.; Garcia, M.; Ivanov, D.

Journal:  Journal of Computational Physics 
Abstract
We present a finitedifference integration algorithm for solution of a system of differential equations containing a diffusion equation with nonlinear terms. The approach is based on CrankNicolson method with predictorcorrector algorithm and provides high stability and precision. Using a specific example of shortpulse laser interaction with semiconductors, we give a detailed description of the method and apply it for the solution of the corresponding system of differential equations, one of which is a nonlinear diffusion equation. The calculated dynamics of the energy density and the number density of photoexcited free carriers upon the absorption of laser energy are presented for the irradiated thin silicon film. The energy conservation within 0.2{\%} has been achieved for the time step {\$}10{\^{}}}4{\$} times larger than that in case of the explicit scheme, for the chosen numerical setup. We also present a few examples of successful application of the method demonstrating its benefits for the theoretical studies of lasermatter interaction problems.