Stability Analysis of Spectral Methods for Hyperbolic Initial-Boundary Value Systems
Stability Analysis of Spectral Methods for Hyperbolic Initial-Boundary Value Systems
We treat a constant coefficient hyperbolic system in one space variable, with zero initial data. Dissipative boundary conditions are imposed at the two points $x = \pm 1$. This problem is discretized either by a spectral or pseudospectral approximation in space. We demonstrate sufficient conditions under which the spectral numerical …