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

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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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Authors and Affiliations

  1. Department of Mathematical Sciences, Kent State University Stark Campus, 6000 Frank Ave NW, North Canton, OH, 44720, USA

    Relja Vulanović

  2. Department for Fundamental Disciplines, Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21000, Novi Sad, Serbia

    Ljiljana Teofanov

Authors
  1. Relja Vulanović
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  2. Ljiljana Teofanov
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Correspondence to Ljiljana Teofanov.

Additional information

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

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Vulanović, R., Teofanov, L. A uniform numerical method for semilinear reaction-diffusion problems with a boundary turning point. Numer Algor 54, 431–444 (2010). https://doi.org/10.1007/s11075-009-9344-6

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  • DOI: https://doi.org/10.1007/s11075-009-9344-6

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