Numerical solution of high-order linear integro-differential equations with variable coefficients using two proposed schemes for rational Chebyshev functions

In this paper, a rational Chebyshev collocation method is presented to solve high-order linear Fredholm integro-differential equations with variable coefficients under the mixed conditions in terms of rational Chebyshev functions by two proposed schemes. The proposed method converts the equation and conditions to matrix equations, by means of collocation points on the semi?infinite interval, which corresponding to systems of linear algebraic equations with rational Chebyshev coefficients. Thus, by solving the matrix equation, rational Chebyshev coefficients are obtained and hence the approximate solution is expressed in terms of rational Chebyshev functions. Numerical examples are given to illustrate the validity and applicability of the method. The proposed method is numerically compared with others existing methods as well as the exact solutions where it maintains better accuracy.