Comparison Chebyshev wavelets method with BPFs method for solving Abel’s integral equation

The aim of this paper is to present an efficient numerical procedure for solving the Abel’s integral equation of the first and second kind and compare it with block-pulse functions (BPFs) method. The proposed method is based on Chebyshev wavelets approximation. This method transforms the integral equation into the matrix equation. The advantages of Chebyshev wavelets are that the values of μ^k and M are adjustable as well as it can yield more accurate numerical solutions than piecewise constant orthogonal functions on the solution of integral equations. The uniform convergence theorem and accuracy estimation are derived and numerical examples show the validity and the wide applicability of the Chebyshev wavelets approach.