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...

Abstract In this paper, by using the local one-dimensional (LOD) method, Taylor series expansion and correction for third derivatives in truncation error remainder, two high-order compact LOD schemes are established solving two- three- dimensional advection equations, respectively. They have fourth-order accuracy both time space. By von Neumann analysis it shows that unconditionally stable. Bes...

in this paper‎, ‎we introduce the notion of $(m,n)$-‎algebr‎aically compact modules as an analogue of algebraically‎ ‎compact modules and then we show that $(m,n)$-algebraically‎ ‎compactness‎ ‎and $(m,n)$-pure injectivity for modules coincide‎. ‎moreover‎, ‎further characterizations of a‎ ‎$(m,n)$-pure injective module over a commutative ring are given‎.

This article is concerned with the fourth-order compact scheme for an accurate simulation of acoustic waves in the frequency domain. The compact schemes are known for a long time; however, they have shown diÆculties, in particular, in dealing with general boundary conditions. This article introduces a new formulation for the compact scheme for the Helmholtz equation and an e ective strategy of ...

We show that smectic order on arbitrary curved substrate can be described by differential form of rank one (1-form), whose geometric meaning is the differential of the local phase field of the density modulation. The exterior derivative of 1-form is shown to be the local dislocation density. Elastic deformations are described by superposition of exact differential forms. More importantly, we us...