A fourth-order finite difference scheme for the numerical solution of 1D linear hyperbolic equation

In this paper, a high-order and unconditionally stable difference method is proposed for the numerical solution of one-space dimensional linear hyperbolic equation. We apply a compact finite difference approximation of fourth-order for discretizing spatial derivative of this equation and a Pade approximation of fifth-order for the resulting system of ordinary differential equations. It is shown through analysis that the proposed scheme is unconditionally stable. This new method is easy to implement, produces very accurate results and needs short CPU time. Some numerical examples are included to demonstrate the validity and applicability of the technique. We compare the numerical results of this paper with the numerical results of some methods in the literature.