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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:
65M06Finite difference methods (IVP of PDE)
76Q05Hydro- and aero-acoustics
76M12Finite volume methods (fluid mechanics)
65M12Stability and convergence of numerical methods (IVP of PDE)
35L45First order hyperbolic systems, initial value problems
65M15Error bounds (IVP of PDE)
Software:
HE-E1GODF
WorldCat.org
Full Text: DOI
References:
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