Rational Chebyshev tau method for solving higher-order ordinary differential equations

An approximate method for solving higher-order ordinary differential equations is proposed. The approach is based on a rational Chebyshev (RC) tau method. The operational matrices of the derivative and product of RC functions are presented. These matrices together with the tau method are utilized to reduce the solution of the higher-order ordinary differential equations to the solution of a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.