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 …

We construct a family of compact fourth order accurate finite difference schemes for the three
dimensional scalar wave (d'Alembert) equation with constant or variable propagation speed …

We consider an initial-boundary value problem for the n-dimensional wave equation with the
variable sound speed, n≥ 1. We construct three-level implicit in time and compact in space …

Reaction–diffusion systems on a spatially heterogeneous domain have been widely used to
model various biological applications. However, solving such partial differential equations …

We compute the scattering of unsteady acoustic waves about complex three-dimensional
bodies with high order accuracy. The geometry of a scattering body is defined with the help …

We propose a high-order time-discretized method for a non-homogeneous linear wave
equation with a forcing term. The method conserves the accumulated discrete energy with …

Efficient and accurate numerical simulation of seismic wave propagation is important in
various Geophysical applications such as seismic full waveform inversion (FWI) problem …

In this paper, we focus on constructing numerical schemes preserving the averaged energy
evolution law for nonlinear stochastic wave equations driven by multiplicative noise. We first …

In this paper, energy-preserving time high-order average vector field (AVF) compact finite
difference scheme is proposed and analyzed for solving two-dimensional nonlinear wave …

In this article, we develop and analyze two energy-preserving high-order average vector
field (AVF) compact finite difference schemes for solving variable coefficient nonlinear wave …