Type: Article
Publication Date: 1987-04-01
Citations: 27
DOI: https://doi.org/10.1137/0724020
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 solution is stable; moreover, these conditions have to be checked only for scalar equations. The stability theorems take the form of explicit bounds for the norm of the solution in terms of the boundary data. The dependence of these bounds on N, the number of points in the domain (or equivalently the degree of the polynomials involved), is investigated for a class of standard spectral methods, including Chebyshev and Legendre collocations.