Control of condition number in Spectral Galerkinimplementation for solving generalized Abel integralequation

Numerical discretization of functional equation using spectral methods usuallyleads to a linear system of algebraic equations with a high conditional and full coefficientmatrix. This drawback destroys the accuracy specially for large values ofapproximation degree. In this paper, we propose a new spectral Galerkin implementationfor solving a class of generalized Abel integral equations, with the purpose ofcontrolling condition number and recovering the familiar spectral accuracy.