Journal of Applied Mathematics
Volume 2012 (2012), Article ID 286391, 13 pages
http://dx.doi.org/10.1155/2012/286391
Research Article

Numerical Solution of Poisson's Equation Using a Combination of Logarithmic and Multiquadric Radial Basis Function Networks

Mohammad Mehdi Mazarei1 and Azim Aminataei2

1Faculty of Engineering, Islamic Azad University, Bushehr Branch, P.O. Box 7519619555, Bushehr, Iran
2Department of Mathematics, K. N. Toosi University of Technology, P.O. Box 15418-49611, Tehran, Iran

Received 27 June 2011; Accepted 18 September 2011

Academic Editor: Roberto Natalini

Copyright © 2012 Mohammad Mehdi Mazarei and Azim Aminataei. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper presents numerical solution of elliptic partial differential equations (Poisson's equation) using a combination of logarithmic and multiquadric radial basis function networks. This method uses a special combination between logarithmic and multiquadric radial basis functions with a parameter 𝑟 . Further, the condition number which arises in the process is discussed, and a comparison is made between them with our earlier studies and previously known ones. It is shown that the system is stable.