Two-dimensional wavelets for numerical solution of integral equations

Abstract

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.