10.1186/2251-7456-6-5

Two-dimensional wavelets for numerical solution of integral equations

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  • Hesam-aldien Derili*1,
  • Saeed Sohrabi2,
  • Asghar Arzhang1,
  1. Department of Mathematics, Karaj Branch, Islamic Azad University, IR
  2. Department of Mathematics, Faculty of Science, Urmia University, IR

Published in Issue 2012-05-28

How to Cite

Derili, H.- aldien, Sohrabi, S., & Arzhang, A. (2012). Two-dimensional wavelets for numerical solution of integral equations. Mathematical Sciences, 6(1). https://doi.org/10.1186/2251-7456-6-5
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Abstract

Abstract Purpose In this paper, we shall investigate the numerical solution of two-dimensional Fredholm integral equations ( 2 D-FIEs). Methods In this work, we apply two-dimensional Haar wavelets, to solve linear two dimensional Fredholm integral equations ( 2 D-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.

Keywords

  • Two-dimensional Fredholm integral equations; Two-dimensional Haar wavelets; Linear systems
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