Chebyshev polynomial solutions of systems of high-order linear differential equations with variable coefficients

Abstract

A Chebyshev collocation method has been presented for numerically solving systems of high-order linear ordinary differential equations with variable coefficients. Using the Chebyshev collocation points, this method transforms the ODE system and the given conditions to matrix equations with unknown Chebyshev coefficients. By means of the obtained matrix equations, a new system of equations which corresponds to the system of linear algebraic equations is gained. Hence, by finding the Chebyshev coefficients easily, the finite Chebyshev series approach is obtained.