On the numerical solution of weakly singular Fredholm integral equations of the second kind using Legendre wavelets-Reference-Cited by-同舟云学术

On the numerical solution of weakly singular Fredholm integral equations of the second kind using Legendre wavelets

Published:2010-09-23 Issue:5 Volume:17 Page:689-698
ISSN:1077-5463
Container-title:Journal of Vibration and Control
language:en
Short-container-title:Journal of Vibration and Control

Author:

Adibi Hojatollah¹,Assari Pouria²

Affiliation:

1. Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran,

2. Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran

Abstract

In this paper, we present a numerical method for solving, linear and nonlinear, weakly singular Fredholm integral equations of the second kind. The method utilizes Legendre wavelets constructed on the unit interval as a basis in the Galerkin method and reduces the solution of the Fredholm integral equation to the solution of a system of algebraic equations. The features of the wavelet coefficient matrices of weakly singular kernels are studied. Finally, numerical examples are presented to show the validity and efficiency of the technique.

Publisher

SAGE Publications

Subject

Mechanical Engineering,Mechanics of Materials,Aerospace Engineering,Automotive Engineering,General Materials Science

Link

http://journals.sagepub.com/doi/pdf/10.1177/1077546310366865

Reference23 articles.

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2. A Class of Bases in $L^2$ for the Sparse Representation of Integral Operators

3. Chebyshev polynomial solutions of systems of linear integral equations

4. Using triangular orthogonal functions for solving Fredholm integral equations of the second kind

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