Necessary conditions for hyperbolic systems

Boundary conditions for hyperbolic equations or systems

Different types of boundary conditions in industrial numerical simulators involving the discretization of hyperbolic systems are presented. For some of them, one may determine the problem to which the limit of approximate solutions (as the discretization parameters tend to 0) is the unique solution. In turn, this convergence result may suggest other ways to take into account the boundary condit...

Necessary Conditions for 2D Systems’ Stability

In this paper we consider parameterized Lyapunov inequalities arising in stability analysis of discrete-discrete and continuous-discrete 2D systems. A necessary condition for their feasibility is presented. This condition is based on an optimization method published earlier by the author. Its properties include being reasonably easy to check, and its coverage being adjustable via the algorithm’...

Some Results on Necessary Conditions for Tow Quasidifferentiable Optimization Problems

New Necessary Conditions for

In this paper, we obtain several nonexistence results for abelian Hadamard diier-ence sets. In particular, we prove that there are no Hadamard diierence sets in abelian groups G = Z 2 Z 2 P , where jPj = p 2 , is odd and p is a prime congruent to 1(mod 4). Also we give a detailed proof for a connection between certain reversible Hadamard diierence sets and projective three-weight codes which wa...

Nonre ecting Boundary Conditions for Linear Hyperbolic Systems 1

Many compressible ow and aeroacoustic computations rely on accurate nonre ecting or radiation boundary conditions. When the equations and boundary conditions are discretized using a nite-di erence scheme, the dispersive nature of the discretized equations can lead to spurious numerical re ections not seen in the continuous boundary value problem. Here we construct discretely nonre ecting bounda...