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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:
65M70Spectral, collocation and related methods (IVP of PDE)
65M12Stability and convergence of numerical methods (IVP of PDE)
35L02First-order hyperbolic equations
65M15Error bounds (IVP of PDE)