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ADER schemes for three-dimensional non-linear hyperbolic systems. (English) Zbl 1060.65641
Summary: We carry out the extension of the ADER approach to multidimensional non-linear systems of conservation laws. We implement non-linear schemes of up to fourth order of accuracy in both time and space. Numerical results for the compressible Euler equations illustrate the very high order of accuracy and non-oscillatory properties of the new schemes. Compared to the state-of-art finite-volume WENO schemes the ADER schemes are faster, more accurate, need less computer memory and have no theoretical accuracy barrier.

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
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