SOLUTION OF INTEGRAL EQUATIONS BY BESSEL WAVELET TRANSFORM

Abstract

The integral equations of the first kind arise in many areas of science and engineering fields such as image processing and electromagnetic theory. The wavelet transform technique to solve integral equation allows the creation of very fast algorithms when compared with known algorithms. Various wavelet methods are used to solve certain type of integral equations. To find the most accurate and stable solution of the integral equation Bessel wavelet is the appropriate method. To study the properties of solution of integral equations on distribution spaces Bessel wavelet transform is also used. In this paper, we accomplished the concept of Hankel convolution and continuous Bessel wavelet transform to solve certain types of integral equations (Volterra integral equation of first kind, Volterra integral equation of second kind and Abel integral equation). Also distributional wavelet transform and generalized convolution will be applied to find the solution of certain Integral equations.