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Fast high order ADER schemes for linear hyperbolic equations. (English) Zbl 1052.65078
Summary: A reformulation of the ADER approach (Arbitrary high order schemes using DERivatives) for linear hyperbolic partial differential equations is presented. This reformulation leads to a drastic decrease of the computational effort. A formula for the construction of ADER schemes that are arbitrary high order accurate in space and time is given. The accuracy for some selected schemes is shown numerically for the two-dimensional linearized Euler equations as a mathematical model for noise propagation in the time domain in aeroacoustics.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76Q05 Hydro- and aero-acoustics
76M12 Finite volume methods applied to problems in fluid mechanics
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L45 Initial value problems for first-order hyperbolic systems
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
Software:
HE-E1GODF
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References:
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