Approximate solution of Abel integral equation in Daubechies wavelet basis

Abstract

This paper presents a new computational method for solving Abel integral equation (both first kind and second kind). The numerical scheme is based on approximations in Daubechies wavelet basis. The properties of Daubechies scale functions are employed to reduce an integral equation to the solution of a system of algebraic equations. The error analysis associated with the method is given. The method is illustrated with some examples and the present method works nicely for low resolution.

Keywords

• abel integral equation
• daubechies scale function
• daubechies wavelet
• gauss-daubechies quadrature rule