Title

A Basis Function for Approximation and the Solutions of Partial Differential Equations

Document Type

Article

Publication Date

5-1-2008

Department

Mathematics

Abstract

In this article, we introduce a type of basis functions to approximate a set of scattered data. Each of the basis functions is in the form of a truncated series over some orthogonal system of eigenfunctions. In particular, the trigonometric eigenfunctions are used. We test our basis functions on recovering the well-known Franke's and Peaks functions given by scattered data, and on the extension of a singular function from an irregular domain onto a square. These basis functions are further used in Kansa's method for solving Helmholtz-type equations on arbitrary domains. Proper one level and two level approximation techniques are discussed. A comparison of numerical with analytic solutions is given. The numerical results show that our approach is accurate and efficient. (C) 2007 Wiley Periodicals, Inc.

Publication Title

Numerical Methods For Partial Differential Equations

Volume

24

Issue

3

First Page

1018

Last Page

1036