Second Kind Chebyshev Wavelet Analysis of Abel’s Integral Equations

Abstract

This paper presents two approximations of the solution functions of Abel’s integral equations belong ing to classes Hα[0,1), Hϕ[0,1) by (λk+1 −1,M)th partial sums of their second kind Chebyshev wavelet expansion in the interval [0,1), for λ > 1. These approximations are E(1) λk+1−1,M (f), E(2) λk+1−1,M (f). Chebyshev wavelets of the second kind were used to solve Abel’s integral equations. The Chebyshev wavelet of the second kind leads to a solution that is almost identical to their exact solution. This research paper’s accomplishment in wavelet analysis is noteworthy.

Keywords

• hα[0, 1),hϕ [0, 1) class, chebyshev wavelet of the second kind, abel's integral equations