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A spectral method of characteristics for hyperbolic problems. (English) Zbl 0743.65080
A spectral method is combined with a timestepping along the characteristics for numerical solution of first-order hyperbolic equations. Theorems about stability and convergence are proved. Numerical examples for one- and two-dimensional problems are given.
Reviewer: M.Fritsche (Jena)

MSC:
65M25 Numerical aspects of the method of characteristics 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
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35L60 First-order nonlinear hyperbolic equations
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