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Error analysis of nonlinear WENO schemes using modified equation. (English) Zbl 1454.65060
Farouk, Mohamed Hesham (ed.) et al., Recent advances in engineering math and physics. Proceedings of the international conference, RAEMP 2019, Cairo, Egypt, December 24–26, 2019. Cham: Springer. 33-46 (2020).
Summary: A theoretical study of the nonlinear weighted essentially non-oscillatory (WENO) method is presented. Single- and multistep explicit numerical time integration algorithms are covered. The main idea is adopting the modified equation method. The necessary lengthy derivations are achieved using a computer algebra system. Accurate theoretical estimates of error norms are derived. The introduced theoretical results are validated via quantitative comparison with numerical experiments.
For the entire collection see [Zbl 1451.74012].
MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
Software:
Maxima
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References:
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