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

Abstract

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