A Basis Function for Approximation and the Solutions of Partial Differential Equations
Document Type
Article
Publication Date
5-1-2008
Department
Mathematics
School
Mathematics and Natural Sciences
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
Recommended Citation
Tian, H. Y.,
Reutskiy, S.,
Chen, C.
(2008). A Basis Function for Approximation and the Solutions of Partial Differential Equations. Numerical Methods For Partial Differential Equations, 24(3), 1018-1036.
Available at: https://aquila.usm.edu/fac_pubs/1518