AVERAGING EINSTEIN'S EQUATIONS: THE LINEARIZED CASE

PML - methods for the linearized Euler equations

A recently suggested method for absorbing boundary conditions for the Euler equations is examined. The method is of PML type and has the important property of being well posed. Results from numerical experiments using a second order discretization are presented. For some choices of parameters the method becomes unstable. The instability is observed to originate from the corner regions. A modifi...

Averaging in Difference Equations

Averaging of Multivalued Differential Equations

where > 0 denotes the small perturbation parameter, t ∈ [0,T/ ] the time variable, z(·) the slow motion, and y(·) the fast motion. The fundamental task in perturbation theory is the construction of a limit system which represents the situation of a vanishing perturbation parameter. In the single-valued case, F(z,y) = {f(z,y)} and G(y) = {g(y)}, that is, in the case of perturbed ordinary differe...

Differential Constraints Compatible with Linearized Equations

Differential constraints compatible with the linearized equations of partial differential equations are examined. Recursion operators are obtained by integrating the differential constraints. One of the standard ways for determining particular solutions to partial differential equations is to reduce them to ordinary differential equations which are easier to solve. The classical work of Lie abo...

Preconditioners for Linearized Discrete Compressible Euler Equations

We consider a Newton-Krylov approach for discretized compressible Euler equations. A good preconditioner in the Krylov subspace method is essential for obtaining an efficient solver in such an approach. In this paper we compare point-block-Gauss-Seidel, point-block-ILU and point-block-SPAI preconditioners. It turns out that the SPAI method is not satisfactory for our problem class. The point-bl...