IJPAM: Volume 46, No. 2 (2008)

Invited Lecture Delivered at
Forth International Conference of Applied Mathematics
and Computing (Plovdiv, Bulgaria, August 12-18, 2007)


NUMERICAL SOLUTION OF WEAKLY SINGULAR
INTEGRAL EQUATIONS BY A GROWING RBF NETWORK

A. Golbabai$^1$, S. Seifollahi$^2$, R. Gholami$^3$
$^{1,2,3}$Department of Mathematics
Islamic Azad University (Karaj Unit)
Rajae Shahr, Karaj, IRAN
$^1$e-mail: golbabai@iust.ac.ir


Abstract.This article presents a new method to solve linear weakly singular Volterra integral equations using radial basis function (RBF) networks. The approximate solution is written as a linear combination of radial basis functions. This method employs a growing RBF network, as the basic approximation element, whose parameters are obtained by optimization of the appropriate error functional composed of the integral equation residue. The simulation results are investigated for the viability of efficiently determining the solution of the integral equation.

Received: August 17, 2007

AMS Subject Classification: 45G05, 45E10, 45L10

Key Words and Phrases: weakly singular integral equation, radial basis function networks, unconstrained optimization

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 46
Issue: 2