Numerical solution using Chebyshev expansion of the higher-orders linear Fredholm integro-differential-difference equations with variable coefficients

The main aim of this paper is to apply the Chebyshev polynomials for the solution of the linear Fredholm integrodifferential- difference equation of high orders. Our approach consists of reducing the problem to a set of linear equations by means of the matrix relations between the Chebyshev polynomials and their derivatives. The operational matrices of delay and derivative together with the Tau method are then utilized to evaluate the unknown coefficients of Chebyshev expansion of the solution.