Numerical solution of a linear Klein-Gordon equation

A new scheme of a linear inhomogeneous Klein-Gordon equation is developed by utilizing finite difference method incorporated with arithmetic mean averaging of functional values. This study considered the central time central space (CTCS) finite difference scheme incorporated with four points arithmetic mean averaging. In addition, the theoretical aspects of finite difference scheme are also considered such as stability, consistency and convergence. The von Neumann stability analysis method and Miller Norm Lemma are used to analyze the stability of the proposed scheme. The performance analysis shows the proposed scheme is stable, consistent and convergent. These theoretical analyses are verified by a numerical experiment. The comparison results shown the proposed scheme produces better accuracy rather than the standard CTCS scheme.