On the stability of Friedrichs’ scheme and the modified Lax-Wendroff scheme

On the Stability of Friedrichs' Scheme and the Modified Lax-Wendroff Scheme*

Necessary and sufficient stability criteria for Friedrichs' scheme and the modified Lax-Wendroff scheme with smooth coefficients are derived by means of Kreiss' Matrix Theorem and the first Stability Theorem of Lax and Nirenberg. In this note we derive necessary and sufficient stability criteria for Friedrichs' scheme and the modified Lax-Wendroff scheme [8] for the hyperbolic system n (1) ". =...

Existence of Discrete Shock Profiles for the Lax-wendroff Scheme

Error Estimates for the Lax — Friedrichs Scheme for Balance Laws

In this paper we extend the result from [9] (V. Jovanović, C. Rohde, Error estimates for finite volume approximations of classical solutions for nonlinear systems of balance laws, SIAM J. Numer. Anal., 43 (2006)), where, among other things, an h — error estimate in the L — norm for the elastodynamics system has been established. We first derive the general error estimate from [9, Theorem 4.4] i...

Lax – Friedrichs sweeping scheme for static Hamilton – Jacobi equations q

We propose a simple, fast sweeping method based on the Lax–Friedrichs monotone numerical Hamiltonian to approximate viscosity solutions of arbitrary static Hamilton–Jacobi equations in any number of spatial dimensions. By using the Lax–Friedrichs numerical Hamiltonian, we can easily obtain the solution at a specific grid point in terms of its neighbors, so that a Gauss–Seidel type nonlinear ite...

More on stochastic and variational approach to the Lax-Friedrichs scheme