A Chebyshev collocation method for the solution of linear integro-differential equations

In this study, a matrix method called the Chebyshev collocation method is presented for numerically solving the linear integro-differential equations by a truncated Chebyshev series. Using the Chebyshev collocation points, this method transforms the integro-differential equation to a matrix equation which corresponds to a system of linear algebraic equations with unknown Chebyshev coefficients. Therefore this allows us to make use of the computer. Also the method can be used for differential and integral equations. To illustrate the method, it is applied to certain linear differential, integral, and integro-differential equations, and the results are compared.