Title: Influence of the Forward Difference Scheme for the Time Derivative on the Stability of Wave Equation Numerical Solution,
Abstract: Research on numerical stability of difference equations has been quite
intensive in the past century. The choice of difference schemes for the
derivative terms in these equations contributes to a wide range of the
stability analysis issues - one of which is how a chosen scheme may directly or
indirectly contribute to such stability. In the present paper, how far the
forward difference scheme for the time derivative in the wave equation
influences the stability of the equation numerical solution, is particularly
investigated. The stability analysis of the corresponding difference equation
involving four schemes, namely Lax's, central, forward, and rearward
differences, were carried out, and the resulting stability criteria were
compared. The results indicate that the instability of the solution of wave
equation is not always due to the forward difference scheme for the time
derivative. Rather, it is shown in this paper that the stability criterion is
still possible when the spatial derivative is represented by an appropriate
difference scheme. This sheds light on the degree of applicability of a
difference scheme for a hyperbolic equation.