Using rationalized Haar wavelet for solving linear integral equations K. Maleknejad * , F. Mirzaee School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, Iran Abstract The main purpose of this paper is to demonstrate that using rationalized Haar wavelet for solving linear Fredholm integral equation of the second kind. We convert the integral equation to a system of linear equations, and by using numerical examples we show our estimation have a good degree of accuracy. Ó 2004 Elsevier Inc. All rights reserved. Keywords: Fredholm integral equations; Operational matrix; Product operation; Rationalized Haar functions 1. Introduction In recent years, many different basic functions have used to the solution of integral equations, such as orthonormal bases and wavelets. The orthogonal set of Haar functions is group of square wave with mag- nitude of þ2 i=2 , 2 i=2 and 0, i ¼ 0; 1; 2; ... [5]. Just these zeros make the Haar transform faster than other square functions such as Walsh function. Lynch and Reis [2] have rationalized the Haar transform by deleting the irrational numbers and introducing the integral powers of two. This modification results in what is called the rationalized Haar (RH) transform. The RH transform preserves all the properties of the original Haar transform and can be efficiently implemented using digital pipline architecture [6]. The corresponding functions * Corresponding author. E-mail addresses: maleknejad@iust.ac.ir (K. Maleknejad), mirzaee@mail.iust.ac.ir (F. Mir- zaee). 0096-3003/$ - see front matter Ó 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2003.11.036 Applied Mathematics and Computation 160 (2005) 579–587 www.elsevier.com/locate/amc