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Applicable Analysis
An International Journal
Volume 94, 2015 - Issue 12
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Articles

A new conservative high-order accurate difference scheme for the Rosenau equation

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Pages 2435-2455 | Received 07 Jul 2014, Accepted 10 Nov 2014, Published online: 08 Dec 2014
 

Abstract

This article is devoted to the study of high-order conservative difference scheme for the Rosenau equation. The difference scheme is two-layered and a seven-point stencil is used for spatial variable. Existence of solutions is shown using a variant of Brouwer fixed point theorem. The unconditional stability as well as uniqueness of the scheme are also derived. The convergence of the difference scheme is proved by utilizing the energy method to be of fourth-order in space and second-order in time in the discrete -norm. Some numerical examples are given in order to validate the theoretical results.

AMS Subject Classifications:

Acknowledgements

The authors would like to thank the editor and the reviewers for their valuable comments.

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