## Journal of Applied Mathematics

- J. Appl. Math.
- Volume 2012 (2012), Article ID 286391, 13 pages.

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

Mohammad Mehdi Mazarei and Azim Aminataei

#### 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.

#### Article information

**Source**

J. Appl. Math., Volume 2012 (2012), Article ID 286391, 13 pages.

**Dates**

First available in Project Euclid: 15 March 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.jam/1331817621

**Digital Object Identifier**

doi:10.1155/2012/286391

**Mathematical Reviews number (MathSciNet)**

MR2854978

**Zentralblatt MATH identifier**

1235.65139

#### Citation

Mazarei, Mohammad Mehdi; Aminataei, Azim. Numerical Solution of Poisson's Equation Using a Combination of Logarithmic and Multiquadric Radial Basis Function Networks. J. Appl. Math. 2012 (2012), Article ID 286391, 13 pages. doi:10.1155/2012/286391. https://projecteuclid.org/euclid.jam/1331817621