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Water wave propagation in unbounded domains. Part II: Numerical methods for fractional PDEs


Jennings, G I; Prigge, D; Carney, S; Karni, S; Rauch, J B; Abgrall, Rémi (2014). Water wave propagation in unbounded domains. Part II: Numerical methods for fractional PDEs. Journal of Computational Physics, 275:443-458.

Abstract

This paper concerns numerical solutions for a fractional partial differential equation arising as a nonreflecting boundary condition in water wave propagation. The fractional derivative operator is written as divergence of a singular integrable convolution, which allows the equation to be viewed as a conservation law with a linear nonlocal flux. A semi-discrete finite volume scheme is presented, using conservative piecewise polynomial reconstruction of the solution. The convolution with the singular kernel is then integrated exactly. Time integration uses Runge–Kutta schemes of matching order. Stability is discussed, convergence is established and numerical examples are presented.

Abstract

This paper concerns numerical solutions for a fractional partial differential equation arising as a nonreflecting boundary condition in water wave propagation. The fractional derivative operator is written as divergence of a singular integrable convolution, which allows the equation to be viewed as a conservation law with a linear nonlocal flux. A semi-discrete finite volume scheme is presented, using conservative piecewise polynomial reconstruction of the solution. The convolution with the singular kernel is then integrated exactly. Time integration uses Runge–Kutta schemes of matching order. Stability is discussed, convergence is established and numerical examples are presented.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:15 October 2014
Deposited On:28 Mar 2018 10:55
Last Modified:13 Apr 2018 11:29
Publisher:Elsevier
ISSN:0021-9991
OA Status:Closed
Publisher DOI:https://doi.org/10.1016/j.jcp.2014.07.007

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