Journal ArticleDOI
Stable Matching of Difference Schemes
TLDR
In this paper, a matching scheme consistent to an equivalent initial boundary value problem was proposed to verify the algebraic conditions for stability of dissipative difference schemes across a coordinate line, and it was shown that some unstable perturbations do not upset the stability of the Lax-Wendroff scheme.Abstract:
Approximations that result from the natural matching of two stable dissipative difference schemes across a coordinate line are shown to be stable. The basic idea is to reformulate the matching scheme consistent to an equivalent initial boundary value problem and to verify the algebraic conditions for stability of such systems. An interesting comparison to the above result is the case of redefinition of a scheme at a single point. In particular, we show that some unstable perturbations do not upset the stability of the Lax–Wendroff scheme.read more
Citations
More filters
Journal ArticleDOI
Upwind Second-Order Difference Schemes and Applications in Aerodynamic Flows
TL;DR: In this article, the authors consider the application of explicit Isecond-order, one-sided or "upwind," difference schemes for the numerical solution of hyperbolic systems in conservation-law form.
Journal ArticleDOI
Stability of interfaces with mesh refinement
TL;DR: Stability for Lax-Wendroff with all the interface conditions considered, and for Leapfrog with interpolation interface conditions when the fine and coarse grids overlap is proved.
Journal ArticleDOI
Fourth Order Difference Methods for the Initial Boundary-Value Problem for Hyperbolic Equations
TL;DR: In this paper, center difference approximations of fourth order in space and second order in time are applied to the mixed initial boundary value problem for the hyperbolic equation u t =-cu.
Journal ArticleDOI
Stability criteria for hybrid difference methods
Johan Larsson,Bertil Gustafsson +1 more
TL;DR: The stability of hybrid difference methods, where different schemes are used in different parts of the domain, is examined and shown that the energy method with the natural norm does not prove stability, but that the Kreiss or 'GKS' theory yields sufficient criteria for stability.
Numerical approximation of boundary conditions with applications to inviscid equations of gas dynamics
TL;DR: A comprehensive overview of the state of the art of wellposedness and stability analysis of difference approximations for initial boundary value problems of the hyperbolic type is presented in this paper.
References
More filters
Journal ArticleDOI
Numerical Solution of Partial Differential Equations.
G. W. Hedstrom,G. D. Smith +1 more
Journal ArticleDOI
Stability theory for difference approximations of mixed initial boundary value problems. I
TL;DR: In this paper, the authors considered the case when the coefficient matrices of the difference schemes were diagonal, and the same class of problems has also been treated in an interesting paper by Osher [2].
Journal ArticleDOI
Systems of difference equations with general homogeneous boundary conditions
TL;DR: In this paper, the authors derived Kreiss' sufficient conditions for stability of dissipative hyperbolic systems with constant coefficients as a corollary to a more general result, in particular, the condition of dissipativity is replaced by a weaker condition.
Journal ArticleDOI
Stability of Difference Approximations to the Mixed Initial Boundary Value Problems for Parabolic Systems
TL;DR: In this article, the stability of difference approximations to a general second order linear parabolic system in one space dimension with given initial and boundary conditions is discussed, and necessary and sufficient conditions on the discrete boundary approximation for stability of the mixed problem are given.
Related Papers (5)
Stability theory of difference approximations for mixed initial boundary value problems. II
Scheme-independent stability criteria for difference approximations of hyperbolic initial-boundary value problems. II
Moshe Goldberg,Eitan Tadmor +1 more