ABSTRACT
A computational approach to solve integral equations is an essential work in scientific research. Integral equations have been one of the essential tools for various areas of applied mathematics. Integral equations occur naturally in many fields of science and engineering [208]. Wavelets theory is a relatively new and emerging area in mathematical research. It has been applied in a wide range of engineering disciplines; particularly, wavelets are very successfully used in signal analysis for waveform representations and segmentations, time frequency analysis, and fast algorithms for easy implementation [53, 54]. Wavelets permit the accurate representation of a variety of functions and operators. Moreover, wavelets establish a connection with fast numerical algorithms. Wavelets can be separated into two distinct types, orthogonal and semi-orthogonal [53, 68]. The research works available in open literature on
wavelets, which were widely used for signal processing, were primarily orthogonal. In signal processing applications, unlike integral equation methods, the wavelet itself is never constructed since only its scaling function and coefficients are needed. However, orthogonal wavelets either have infinite support or a non-symmetric, and in some cases fractal, nature. These properties can make them a poor choice for characterization of a function. In contrast, the semi-orthogonal wavelets have finite support, both even and odd symmetry, and simple analytical expressions, ideal attributes of a basis function [148].
