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Journal of Scientific Computing
Published in: Journal of Scientific Computing 1/2020

01-04-2020

Optimal Error Estimate of the Extended-WKB Approximation to the High Frequency Wave-Type Equation in the Semi-classical Regime

Authors: Chunxiong Zheng, Jiashun Hu

Published in: Journal of Scientific Computing | Issue 1/2020

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Abstract

For the Cauchy problem of the high frequency wave-type equation with Wentzel–Kramers–Brillouin (WKB) type initial data, the extended Wentzel–Kramers–Brillouin (E-WKB) ansatz is an asymptotically valid solution. This ansatz is globally defined and formulated as an integral of coherent states over the displaced Lagrangian submanifold. This paper proves the optimal first order error estimate of the proposed E-WKB ansatz in \(L^2\) norm for the wave-type equation in the semi-classical regime. The key ingredients in the proof are the moving frame technique developed in Zheng (Commun Math Sci 11:105–140, 2013) and the deep relations between the E-WKB analysis and the classical WKB analysis. Numerical results on the linear KdV equation verify the theoretical analysis.
previous article A Computational Comparison Between Isogeometric Analysis and Spectral Element Methods: Accuracy and Spectral Properties
next article A Linearly Implicit Structure-Preserving Scheme for the Camassa–Holm Equation Based on Multiple Scalar Auxiliary Variables Approach

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Appendix
Available only for authorised users
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Metadata
Title
Optimal Error Estimate of the Extended-WKB Approximation to the High Frequency Wave-Type Equation in the Semi-classical Regime
Authors
Chunxiong Zheng
Jiashun Hu
Publication date
01-04-2020
Publisher
Springer US
Published in
Journal of Scientific Computing / Issue 1/2020
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-020-01208-x

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