Original research
Two-dimensional wavelets for numerical solution of integral equations
1 Department of Mathematics, Karaj Branch, Islamic Azad University, P.O. Box 31485-313, Iran
2 Department of Mathematics, Faculty of Science, Urmia University, Iran
Mathematical Sciences 2012, 6:5 doi:10.1186/2251-7456-6-5
Published: 28 May 2012Abstract
Purpose
In this paper, we shall investigate the numerical solution of two-dimensional Fredholm integral equations (2D-FIEs).
Methods
In this work, we apply two-dimensional Haar wavelets, to solve linear two dimensional Fredholm integral equations (2D-FIEs). Using 2D Haar wavelets and their properties, 2D-FIEs of the second kind reduce to a system of algebraic equations.
Results
The numerical examples illustrate the efficiency and accuracy of the method.
Conclusions
In comparison with other bases (for example, polynomial bases), one of the advantages of this method is, although the involved matrices have a large dimension, they contain a large percentage of zero entries, which keeps computational effort within reasonable limits.
