http://dx.doi.org/10.1016/j.camwa.2003.06.010">
 

Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Multiquadric collocation method with integral formulation for boundary layer problems

Language

English

Abstract

Singularly perturbed boundary value problems often have solutions with very thinlayers in which the solution changes rapidly. This paper concentrates on the case where theses layers occur near the boundary, although our method can be applied to problems with interior layers. One technique to deal with the increased resolution requirements in these layers is the use of domain transformations. A coordinate stretching based transform allows to move collocation points into the layer, a requirement to resolve the layer accurately. Previously, such transformations have been studied in the context of finite-difference and spectral collocation methods. In this paper, we use radial basis functions (RBFs) to solve the boundary value problem. Specifically, we present a collocation method based on multiquadric (MQ) functions with an integral formulation combined with a coordinate transformation. We find that our scheme is ultimately more accurate than a recently proposed adaptive MQ scheme. The RBF scheme is also amenable to adaptivity. © 2004 Elsevier Ltd. All rights reserved.

Keywords

Boundary layer, Boundary layer problems, High-order discretizations, Integral formulation, Multiquadric, Spectral accuracy

Publication Date

2004

Source Publication Title

Computers and Mathematics with Applications

Volume

48

Issue

6-5

Start Page

927

End Page

941

Publisher

Elsevier

ISSN (print)

08981221

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