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Numerical implementation of the sinc-Galerkin method for second-order hyperbolic equations. (English) Zbl 0698.65069

Summary: A fully Galerkin method in both space and time is developed for the second-order, linear hyperbolic problem. Sinc basis functions are used and error bounds are given which show the exponential convergence rate of the method. The matrices necessary for the formulation of the discrete system are easily assembled. They require no numerical integrations (merely point evaluations) to be filled.

The discrete problem is formulated in two different ways and solution techniques for each are described. Consideration of the two formulations is motivated by the computational architecture available. Each has advantages for the appropriate hardware. Numerical results reported show that if 2N+1 basis functions are used then the exponential convergence rate 0[exp(-κ N)], κ>0, is attained for both analytic and singular problems.

MSC:
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65N15Error bounds (BVP of PDE)
35L20Second order hyperbolic equations, boundary value problems