This paper discusses compact-stencil nite difference time domain (FDTD) schemes for approximating the 2D wave equation in the context of digital audio. Stability, accuracy, and ef ciency are investigated and new ways of viewing and interpreting the results are discussed. It is shown that if a tight accuracy constraint is applied, implicit schemes outperform explicit schemes. The paper also disc...

We consider compact finite-difference schemes of the 4th approximation order for an initial-boundary value problem (IBVP) n-dimensional nonhomogeneous wave equation, n? 1. Their construction is accomplished by both classical Numerov approach and alternative technique based on averaging together with further necessary improvements arising scheme 2. The applicable to other types PDEs including pa...

High order integro-differential equations (IDE), especially nonlinear, are usually difficult to solve even for approximate solutions. In this paper, we give a high accurate compact finite difference method to efficiently solve integro-differential equations, including high order and nonlinear problems. By numerical experiments, we show that compact finite difference method of integro-differenti...