Numerical solution of Volterra integro-differential equations by the Tau method with the Chebyshev and Legendre bases

In this paper we present a solution to the Volterra integro-differential equations (VIDE) by the Tau method with arbitrary polynomial bases. We apply some simple matrices in extension of the Tau method for the numerical solution of VIDE. In particular the Chebyshev and Legendre polynomials are applied as the bases polynomials. The results of examples are illustrated that the Tau method bases are very useful in computing a numerical solution of VIDE.