Numerical Solution of System of Higher Order Linear Ordinary Differential Equations with Variable Coefficients Using Two Proposed Schemes for Rational Chebyshev Functions

The purpose of this paper is to investigate the use of rational Chebyshev collocation method for solving systems of high-order linear ordinary differential equations with variable coefficients by two schemes. Using the rational Chebyshev collocation points, these methods transform the system of high-order linear ordinary differential equations and the given conditions to matrix equations with unknown rational 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. Numerical examples are given to illustrative the validity and applicability of the method. The proposed method, in these two schemes, is numerically compared with others existing methods where it maintains better accuracy.