A uniform numerical method for semilinear reaction-diffusion problems with a boundary turning point |
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Authors: | Relja Vulanović Ljiljana Teofanov |
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Affiliation: | 1.Department of Mathematical Sciences,Kent State University Stark Campus,North Canton,USA;2.Department for Fundamental Disciplines, Faculty of Technical Sciences,University of Novi Sad,Novi Sad,Serbia |
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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. |
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