Gideon Zwas

Self-adjusting hybrid schemes for shock computations

Abstract A general approach for constructing “hybrid schemes” in order to solve quasilinear hyperbolic initial-value problems is presented. The hybrid schemes are constructed from a first-order accuracy operator which dominates in shock regions and a higher-order operator which produces more accurate results in smooth regions. The usefulness and accuracy of the method is demonstrated in one- and two-dimensional examples, while overcoming nonlinear instabilities and post-shock oscillations.

Switched numerical Shuman filters for shock calculations

SummaryWhen using Shumans filtering operator in the numerical computation of shock waves, nonlinear instabilities are prevented, but high order accuracy is lost even in smooth regions. In order to preserve second or higher order accuracy in these regions, an automatic switched Shuman filter is constructed. Nonsteady shock calculations in one and two spatial dimensions, demonstrate the usefulness and accuracy of the method, including examples with third and fourth order accurate finite difference schemes.

Numerical stabilizers and computing time for second-order accurate schemes☆

Abstract This paper deals with explicit second-order accurate schemes for solving quasilinear hyperbolic equations with two spatial dimensions. The effect of certain stabilizing terms that allow a larger time step is studied and numerical examples are given, taking into account the simplicity of the schemes so as to shorten the actual computing time.

On matrices having equal spectral radius and spectral norm

Abstract In this paper we characterize all n x n matrices whose spectral radius equals their spectral norm. We show that for n ⩾3 the class of these matrices contains the normal matrices as a subclass.

On two step Lax-Wendroff methods in several dimensions

AbstractA version of Richtmyers two step Lax-Wendroff scheme for solving hyperbolic systems in conservation form, is considered. This version uses only the nearest points, has second order accuracy at every time cycle and allows a time step which is larger by a factor of

Numerical radius of positive matrices

\sqrt d

Area approximations in the mathematical laboratory

than Richtmyers, whered is the number of spatial dimensions. The scheme appears to be competitive with the optimal stability schemes proposed by Strang and carried out by Gourlay and Morris.

Computer root extraction by a priori design

In this paper we investigate spectral matrices, i.e., matrices with equal spectral and numerical radii. Various characterizations and properties of these matrices are given.