Several studies have presented compact fourth order accurate finite difference
approximation for the Helmholtz equation in two or three dimensions. Several of these …

Sixth-order quasi-compact difference (QCD) schemes are proposed for the two-dimensional
(2D) and the three-dimensional (3D) Helmholtz equations with the variable parameter. Our …

We consider fourth order accurate compact schemes, in both space and time, for the second
order wave equation with a variable speed of sound. We demonstrate that usually this is …

A new augmented method is proposed for elliptic interface problems with a piecewise
variable coefficient that has a finite jump across a smooth interface. The main motivation is to …

Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media
is crucial to seismic modeling, imaging and inversion. Actually, it represents the core …

High order methods are preferred in many applications such as Helmholtz equations with
large wave numbers to resolve the solution numerically. In this paper, a third order compact …

In this paper, we reconsider the inverse Lax-Wendroff (ILW) procedure, which is a numerical
boundary treatment for solving hyperbolic conservation laws, and propose a new approach …

The purpose of this note… is to sort out my own thoughts… and to solicit ideas from others.
Lloyd N. Trefethen Three mysteries of Gaussian elimination Since 2008, when the first …

In this paper, a compact finite difference scheme with global convergence order O\big (τ^ 2-
α+ h^ 4\big) O (τ 2-α+ h 4) is derived for fractional sub-diffusion equations with the spatially …

We describe a high-order accurate methodology for the numerical simulation of time-
harmonic waves governed by the Helmholtz equation. Our approach combines compact …