Stability of two-dimensional initial-boundary value problems using leap-frog type schemes

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

Stability of Finite Difference Schemes for Hyperbolic Initial Boundary Value Problems: Numerical Boundary Layers

In this article, we give a unified theory for constructing boundary layer expansions for discretized transport equations with homogeneous Dirichlet boundary conditions. We exhibit a natural assumption on the discretization under which the numerical solution can be written approximately as a two-scale boundary layer expansion. In particular, this expansion yields discrete semigroup estimates tha...

Stability of Finite Difference Schemes for Hyperbolic Initial Boundary Value Problems

The aim of these notes is to present some results on the stability of finite difference approximations of hyperbolic initial boundary value problems. We first recall some basic notions of stability for the discretized Cauchy problem in one space dimension. Special attention is paid to situations where stability of the finite difference scheme is characterized by the so-called von Neumann condit...

Semigroup stability of finite difference schemes for multidimensional hyperbolic initial-boundary value problems

We develop a simple energy method for proving the stability of finite difference schemes for multidimensional hyperbolic initial-boundary value problems. In particular, we extend to several space dimensions and to variable coefficients a crucial stability result by Goldberg and Tadmor for Dirichlet boundary conditions. This allows us to give some conditions on the discretized operator that ensu...

approximating initial-value problems with two-point boundary-value problems: bbm-equation