NDLI: A convergent finite difference scheme for the Ostrovsky-Hunter equation on a bounded domain

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A convergent finite difference scheme for the Ostrovsky-Hunter equation on a bounded domain

Content Provider	Springer Nature Link
Author	Risebro, N. H. Coclite, G. M. Ridder, J.
Copyright Year	2016
Abstract	We prove the convergence of a finite difference scheme to the unique entropy solution of a general form of the Ostrovsky-Hunter equation on a bounded domain with periodic boundary conditions. The equation models, for example, shallow water waves in a rotating fluid and ultra-short light pulses in optical fibres, and its solutions can develop discontinuities in finite time. Our scheme extends monotone schemes for conservation laws to this equation. The convergence result also provides an existence proof for periodic entropy solutions of the general Ostrovsky-Hunter equation. Uniqueness and an $${\mathscr {O}}({\varDelta x}^{1/2})$$ bound on the $$L^1$$ error of the numerical solutions are shown using Kružkov’s technique of doubling of variables and a “Kuznetsov type” lemma. Numerical examples confirm the convergence results.
Ending Page	122
Page Count	30
Starting Page	93
File Format	PDF
ISSN	00063835
e-ISSN	15729125
Journal	BIT Numerical Mathematics
Issue Number	1
Volume Number	57
Language	English
Publisher	Springer Netherlands
Publisher Date	2016-07-20
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Computational Mathematics and Numerical Analysis Stability Uniqueness Numeric Computing Mathematics Monotone scheme Vakhnenko equation Short-pulse equation Convergence Ostrovsky-Hunter equation Initial-boundary value problems for systems of mixed type Initial-boundary value problems for higher-order hyperbolic equations Existence Finite difference methods Entropy solution
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Networks and Communications Computational Mathematics Software

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