A Chebyshev polynomial approach for linear Fredholm–Volterra integro-differential equations in the most general form

The main purpose of this article is to present an approximation method for higher order linear Fredholm–Volterra integro-differential equations (FVIDE) in the most general form under the mixed conditions in terms of Chebyshev polynomials. This method transforms FVIDE and the conditions into the matrix equations which correspond to a system of linear algebraic equations with unknown Chebyshev coefficients. Finally, some examples are presented to illustrate the method and the results are discussed.