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A class of singularly perturbed semilinear differential equations with interior layers


Authors: P. A. Farrell, E. O'Riordan and G. I. Shishkin
Journal: Math. Comp. 74 (2005), 1759-1776
MSC (2000): Primary 65L70, 65L20, 65L10, 65L12
DOI: https://doi.org/10.1090/S0025-5718-05-01764-3
Published electronically: June 7, 2005
MathSciNet review: 2164095
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Abstract: In this paper singularly perturbed semilinear differential equations with a discontinuous source term are examined. A numerical method is constructed for these problems which involves an appropriate piecewise-uniform mesh. The method is shown to be uniformly convergent with respect to the singular perturbation parameter. Numerical results are presented that validate the theoretical results.


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Additional Information

P. A. Farrell
Affiliation: Department of Computer Science, Kent State University, Kent, Ohio 44242, U.S.A.
Email: farrell@cs.kent.edu

E. O'Riordan
Affiliation: School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland
Email: eugene.oriordan@dcu.ie

G. I. Shishkin
Affiliation: Institute of Mathematics and Mechanics, Russian Academy of Sciences, Ekaterinburg, Russia
Email: shishkin@imm.uran.ru

DOI: https://doi.org/10.1090/S0025-5718-05-01764-3
Keywords: Semilinear, reaction-diffusion, interior layer, piecewise-uniform mesh
Received by editor(s): October 13, 2003
Received by editor(s) in revised form: June 11, 2004
Published electronically: June 7, 2005
Additional Notes: This research was supported in part by the Albert College Fellowship Scheme of Dublin City University, by the Enterprise Ireland grant SC–2000–070 and by the Russian Foundation for Basic Research under grant No. 04–01–00578.
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.