The Golden Section Search Algorithm for Finding a Good Shape Parameter for Meshless Collocation Methods

Document Type

Article

Publication Date

8-1-2010

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

In this paper we propose to apply the golden section search algorithm to determining a good shape parameter of multiquadrics (MQ) for the solution of partial differential equations. We use two radial basis function based meshless collocation methods, the method of approximate particular solutions (MAPS) and Kansas method, to solve partial differential equations. Due to the severely ill-conditioned matrix system using MQ we also consider the truncated singular value decomposition method (TSVD) to regularize the smoothness of the error versus shape parameter curve so that a reasonably good shape parameter can be identified. We also analyze cost and accuracy for using LU decomposition and TSVD. Numerical results show that the proposed golden section search method is effective and provides a reasonable shape parameter along with acceptable accuracy of the solution. (C) 2010 Elsevier Ltd. All rights reserved.

Publication Title

Engineering Analysis With Boundary Elements

Volume

34

Issue

8

First Page

738

Last Page

746

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