Two-Dimensional Legendre Wavelets and their Applications to Integral Equations

Abstract

The main focus of this paper is to present an effective numerical method for solving two-dimensional Fredholm integral equations, which appear in many phenomena in physics and engineering. For this purpose, a new set of two-dimensional wavelets is constructed by Legendre polynomials. The properties of the novelty wavelets are studied. The suggested method reduces a two-dimensional Fredholm integral equation to an algebraic equations system. Furthermore, to illustrate uniform convergence and accuracy of these wavelets, some theorems are proved. The method is applied on some examples to confirm its accuracy and computational efficiency.