Search
Results
-
Stability of time discretization, Hurwitz determinants and order stars
(1995)SAM Research ReportWe shall review stability requirements for time discretizations of ordinary and partial differential equations. If a constant time step is used and the method involves more than two time levels stability is always related to the location of roots of a polynomial in circular or half plane regions. In several cases the coefficients of the polynomial depend on a real or complex parameter. Hurwitz determinants allow to create a fraction free ...Report -
An Accuracy Barrier for Stable Three-Time-Level Difference Schemes for Hyperbolic Equations
(1995)SAM Research ReportWe consider three-time-level difference schemes for the linear constant coefficient advection equation $u_t = cu_x$. In 1985 it was conjectured that the varrier to the local order $p$ of schemes which are stable is giben by $p \le 2$ min {$R$,$S$}. Here $R$ and $S$ denote the number of downwind and upwind points, respectively, in the difference stencil with respect to the characteristic of the differential equation through the update ...Report -
Multidimensional schemes for nonlinear systems of hyperbolic conservation laws
(1995)SAM Research ReportMost commonly used schemes for unsteady multidimensional systems of hyperbolic conservation laws use dimensional splitting. In each coordinate direction a scheme for a one dimensional system is used. Such an approach does not take in account the infinitely many propagation directions which are present in a system in several space dimensions. In 1992 M. Fey introduced what he called the Method of Transport, MoT, for the Euler equations of ...Report