Solution of Abel's integral equation by modified Taylor wavelet with error analysis

Abstract

In this paper, a modified Taylor wavelet (MTW) is introduced. Three new estimators $ E_{2^{k-1},M}^{(1)}(f) $, $ E_{2^{k-1},M}^{(2)}(f) $ and $ E_{2^{k-1},M}^{(3)}(f) $ of functions of H$ \ddot{\text{o}} $lder's class $ H^{\alpha} [0,1) $ of order $ 0<\alpha \leq 1 $ have been established by MTW method. A MTW method is presented for the numerical solution of Abel's integral equations. MTW operational matrices are formulated. These matrices have been utilized for solving Abel's integral equations. Some examples are included to demonstrate the validity and efficiency of the proposed method.