An Exponential Time Differencing Method for the Kuramoto-Sivashinsky Equation

Gentian Zavalani

An Exponential Time Differencing Method for the Kuramoto-Sivashinsky Equation

Gentian Zavalani * §

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Polytechnic University of Tirana

An Exponential Time Differencing Method for the Kuramoto-Sivashinsky Equation

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Abstract

The spectral methods offer very high spatial resolution for a wide range of nonlinear wave equations, so, for the best computational efficiency, it should be desirable to use also high order methods in time but without very strict restrictions on the step size by reason of numerical stability. In this paper we study the exponential time differencing fourth-order Runge-Kutta (ETDRK4) method; this scheme was derived by Cox and Matthews in [S.M. Cox, P.C. Matthews, Exponential time differencing for stiff systems, J. Comp. Phys. 176 (2002) 430-455] and was modified by Kassam and Trefethen in [A. Kassam, L.N. Trefethen, Fourth-order time stepping for stiff PDEs, SIAM J. Sci. Comp. 26 (2005Comp. 26 ( ) 1214Comp. 26 ( -1233]]. We compute its amplification factor and plot its stability region, which gives us an explanation of its good behavior for dissipative and dispersive problems. We apply this method to the Kuramoto-Sivashinsky Equation obtaining excellent results.

References

24 Cites in Article

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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

How to Cite This Article

Gentian Zavalani. 2014. "An Exponential Time Differencing Method for the Kuramoto-Sivashinsky Equation". Global Journal of Research in Engineering - I: Numerical Methods GJRE-I Volume 14 (GJRE Volume 14 Issue I1).

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GJRE Volume 14 Issue I1

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Journal Specifications

Crossref Journal DOI 10.17406/gjre

Print ISSN 0975-5861

e-ISSN 2249-4596

Keywords

etd ETDRK4 integrating factor kuramoto-sivashinsky stiff systems

Classification

GJRE-I Classification FOR Code: 230199

010301p

Submission ReceivedDecember 13, 2013
Peer Review Double Blind
Handling Editor
Accepted January 3, 2014
Published January 15, 2014

Version of record

v1.2

Issue date

June 30, 2014

Language

English

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Article Matrices

Total Score: 101

Country: Albania

Subject: Global Journal of Research in Engineering

Authors: Gentian Zavalani (PhD/Dr. count: 0)

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