Sayyed Rasoul Kafi - Department of Mathematics, Shiraz University of Technology, Shiraz, Iran
Payam Mokhtary - Department of Mathematics, Sahand University of Technology, Tabriz, Iran
Esmail Hesameddini - Department of Mathematics, Shiraz University of Technology, Shiraz, Iran

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.

Generalized Abel integral equation, spectral Galerkin, condition number