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Boundary integral methods for singularly perturbed boundary value problems

Langdon, S. and Graham, I. G. (2001) Boundary integral methods for singularly perturbed boundary value problems. IMA Journal of Numerical Analysis, 21 (1). pp. 217-237. ISSN 1464-3642

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To link to this article DOI: 10.1093/imanum/21.1.217

Abstract/Summary

In this paper we consider boundary integral methods applied to boundary value problems for the positive definite Helmholtz-type problem -DeltaU + alpha U-2 = 0 in a bounded or unbounded domain, with the parameter alpha real and possibly large. Applications arise in the implementation of space-time boundary integral methods for the heat equation, where alpha is proportional to 1/root deltat, and deltat is the time step. The corresponding layer potentials arising from this problem depend nonlinearly on the parameter alpha and have kernels which become highly peaked as alpha --> infinity, causing standard discretization schemes to fail. We propose a new collocation method with a robust convergence rate as alpha --> infinity. Numerical experiments on a model problem verify the theoretical results.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical and Physical Sciences > Department of Mathematics and Statistics
No Reading authors. Back catalogue items
ID Code:26173
Uncontrolled Keywords:singular perturbation, boundary integral method, Helmholtz equation, heat equation, collocation, trigonometric polynomial
Publisher:Oxford University Press

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