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A Legendre spectral method in time for first-order hyperbolic equations. (English) Zbl 1175.65121

Summary: We take first-order hyperbolic equations with periodic boundary conditions as a model to present a Legendre spectral method in time with Fourier approximation in spacel. Convergence analysis of the spectral scheme is given and the \(L^2\)-optimal error estimate in space is achieved. Also, the method is valid for variable coefficient case. Numerical results show the efficiency of the method.

MSC:

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
35L02 First-order hyperbolic equations
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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