Numerical solution of Abel’s integral equation by using Legendre wavelets

A numerical method for solving Abel’s integral equation as singular Volterra integral equations is presented. The method is based upon Legendre wavelet approximations. The properties of Legendre wavelet are first presented. These properties are then utilized to reduce the singular Volterra integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.