Chebyshev-Tau method for the linear Klein-Gordon equation

Abstract

In this paper, we study a numerical method based on polynomial approximation, using the shifted Chebyshev polynomial, to construct the approximate solutions of the one dimensional linear Klein-Gordon equation with constant coefficients. Also, we give general forms of the operational matrices of integral and derivative. We solve two illustrative examples to test this method known as the shifted Chebyshev Tau method. By using this method, the problem is reduced to a set of linear algebraic equations by the operational matrices of integral and derivative. Then, solving the systems, we obtain the exact solutions to these problems. It is shown that the method produces accurate results. Key words: Chebyshev polynomials, Tau method, shifted Chebyshev series, Klein-Gordon equation.