A Second Kind Chebyshev Polynomial Approach for the Wave Equation Subject to an Integral Conservation Condition

Abstract

The main purpose of this article is to present an approximate solution for the one dimensional wave equation subject to an integral conservation condition in terms of second kind Chebyshev polynomials. The operational matrices of integration and derivation are introduced and utilized to reduce the wave equation and the conditions into the matrix equations which correspond to a system of linear algebraic equations with unknown Chebyshev coefficients. Finally, some examples are presented to illustrate the applicability of the method.