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Numerical AlgorithmsVolume 54, Issue 4, 2010, Pages 431-444

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

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  • aDepartment of Mathematical Sciences, Kent State University Stark Campus, 6000 Frank Ave NW, North Canton, OH 44720, United States
  • bDepartment for Fundamental Disciplines, Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21000 Novi Sad, Serbia

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.

Author keywords

Boundary turning pointFinite-difference methodLayer-adapted meshOne-dimensional reaction-diffusion problemSemilinear boundary-value problemSingular perturbation

Funding details

Funding sponsor Funding number Acronym
Ministarstvo Prosvete, Nauke i Tehnološkog Razvoja144006MPNTR

  • 1

    The second author’s work was supported by the Ministry of Science and Technological Development of the Republic of Serbia under grant 144006.

  • ISSN: 10171398
  • Source Type: Journal
  • Original language: English
  • DOI: 10.1007/s11075-009-9344-6
  • Document Type: Article

  Teofanov, L.; Department for Fundamental Disciplines, Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, Serbia;
© Copyright 2010 Elsevier B.V., All rights reserved.

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