A uniform numerical method for semilinear reaction-diffusion problems with a boundary turning point

Abstract

Motivated by problems arising in semiconductor-device modeling, this paper is concerned with a singularly perturbed semilinear reaction-diffusion problem with a boundary turning point. It is proved that the problem has a unique solution with two boundary layers. Based on the estimates of the derivatives of the solution, a numerical method is proposed which uses the classical finite-difference discretization on a Bakhvalov-type mesh. Second-order accuracy, uniform with respect to the perturbation parameter, is proved in the maximum norm. Numerical results are presented in support of the theoretical ones. © 2009 Springer Science+Business Media, LLC.