http://dx.doi.org/10.1016/j.camwa.2006.04.009">
 

Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

The role of the multiquadric shape parameters in solving elliptic partial differential equations

Language

English

Abstract

This study examines the generalized multiquadrics (MQ), φj(x) = [(x-xj)2+cj 2] β in the numerical solutions of elliptic two-dimensional partial differential equations (PDEs) with Dirichlet boundary conditions. The exponent β as well as cj 2 can be classified as shape parameters since these affect the shape of the MQ basis function. We examined variations of β as well as cj 2 where cj 2 can be different over the interior and on the boundary. The results show that increasing,β has the most important effect on convergence, followed next by distinct sets of (cj 2)Ω∂Ω ≪ (cj 2)∂Ω. Additional convergence accelerations were obtained by permitting both (cj 2)Ω∂Ω and (cj 2)∂Ω to oscillate about its mean value with amplitude of approximately 1/2 for odd and even values of the indices. Our results show high orders of accuracy as the number of data centers increases with some simple heuristics. © 2006 Elsevier Ltd.

Keywords

Different shape parameters, Elliptic PDEs, Generalized multiquadrics

Publication Date

2006

Source Publication Title

Computers and Mathematics with Applications

Volume

51

Issue

8

Start Page

1335

End Page

1348

Publisher

Elsevier

ISSN (print)

08981221

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