Two-Dimensional Legendre Wavelets and Their Applications to Integral Equations

Masood Roodaki; Zahra JafariBehbahani

doi:10.17485/ijst/2015/v8i2/58075

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Two-Dimensional Legendre Wavelets and Their Applications to Integral Equations

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2015/v8i2/58075

Year: 2015, Volume: 8, Issue: 2, Pages: 157–164

Original Article

Two-Dimensional Legendre Wavelets and Their Applications to Integral Equations

Masood Roodaki^* , Zahra JafariBehbahani

Department of Mathematics, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran; roodaki_1436@yahoo.com

This work is licensed under a Creative Commons Attribution 4.0 International License.

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.

Keywords:
Direct Method, Legendre Polynomials, Legendre Wavelets, Two-Dimensional Fredholm Integral Equations, Operational Matrix