CAS Wavelet and its Applications in Approximation of a function belonging to Holder's class Hα [0; 1) and Solution of Fredholm Integral Equation of Second Kind

Abstract

In this paper, cosine and sine wavelet is considered. Two new CAS wavelet estimators E(1) 2k;2M+1(f) and E(2) 2k;2M+1(f) for the approximation of a function f whose first derivative f' and second derivative f '' belong to Hölder's class Hα [0; 1) of order 0 <α≤1, have been obtained. These estimators are sharper and best in wavelet analysis.Using CAS wavelet a computational method has been developed to solve Fredholm integral equation of second kind. In this process, Fredholm integral equations are reduced into a system of linear equations. Approximation of function by CAS wavelet method is applied in obtaining the solution of Fredholm integral equation of second kind. CAS wavelet coefficient matrices are prepared using the properties of CAS wavelets.Two examples are illustrated to show the validity and efficiency of the technique discussed in this paper.

Keywords

• cas wavelet, cas wavelet approximation, function of holder's class, orthonormal basis, fredholm integral equation