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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A class of singularly perturbed quasilinear differential equations with interior layers


Authors: P. A. Farrell, E. O’Riordan and G. I. Shishkin
Journal: Math. Comp. 78 (2009), 103-127
MSC (2000): Primary 65L20; Secondary 65L10, 65L12, 34B15
Published electronically: June 27, 2008
MathSciNet review: 2448699
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Abstract | References | Similar Articles | Additional Information

Abstract: A class of singularly perturbed quasilinear differential equations with discontinuous data is examined. In general, interior layers will appear in the solutions of problems from this class. A numerical method is constructed for this problem class, which involves an appropriate piecewise-uniform mesh. The method is shown to be a parameter-uniform numerical method with respect to the singular perturbation parameter. Numerical results are presented, which support the theoretical results.


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Additional Information

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

E. O’Riordan
Affiliation: School of Mathematical Sciences, Dublin City University, 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: http://dx.doi.org/10.1090/S0025-5718-08-02157-1
PII: S 0025-5718(08)02157-1
Keywords: Quasilinear, uniform convergence, layer adapted mesh, interior layer
Received by editor(s): April 2, 2007
Received by editor(s) in revised form: December 7, 2007
Published electronically: June 27, 2008
Additional Notes: This research was supported in part by the Mathematics Applications Consortium for Science and Industry in Ireland (MACSI) under the Science Foundation Ireland (SFI) mathematics initiative. The third author was supported in part by the Russian Foundation for Basic Research under grant No. 07–01–00729.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.