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Domain decomposition methods for systems of conservation laws: Spectral collocation approximations. (English) Zbl 0711.65082

The author proposes an effective domain decomposition method for the numerical solution of quasi-linear hyperbolic systems of conservation laws. The method is designed for a general nonlinear problem in several space variables. Convergence analysis is carried out and the precise form of the error-reduction factor is derived. An application of the proposed method is indicated.
Reviewer: P.K.Mahanti

MSC:

65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
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