Convergence of spectral methods for hyperbolic initial-boundary value systems. (English) Zbl 0622.65110

Gottlieb, David; Lustman, Liviu; Tadmor, Eitan

SIAM J. Numer. Anal. 24, 532-537 (1987).

Results obtained by the same authors in a previous paper [NASA Contractors Report #178035, ICASE Report #86.2] apply spectral methods to initial boundary value problems for hyperbolic equations. Those approximations are shown to converge to the exact solutions, at least when those solutions are smooth. The numerical error is bounded. Using Gauss-Lobatto quadrature formulae the error is obtained for a single equation and this bound is used to find the overall error of the system.

Reviewer: W.Ames

MSC:

65N35	Spectral, collocation and related methods for boundary value problems involving PDEs
35L50	Initial-boundary value problems for first-order hyperbolic systems

Keywords:

convergence; stability; collocation; spectral methods