Fourier Spectral Methods for Numerical Solving of the Kuramoto-Sivashinsky Equation

Gentian Zavalani

Fourier Spectral Methods for Numerical Solving of the Kuramoto-Sivashinsky Equation

Gentian Zavalani * §

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§ Polytechnic University of Tirana/ Albania

Fourier Spectral Methods for Numerical Solving of the Kuramoto-Sivashinsky Equation

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Abstract

In this paper I presented a numerical technique for solving Kuramoto-Sivashinsky equation, based on spectral Fourier methods. This equation describes reaction diffusion problems, and the dynamics of viscous-fuid films flowing along walls. After we wrote the equation in Furie space, we get a system. In this case, the exponential time differencing methods integrate the system much more accurately than other methods since the exponential time differencing methods assume in their derivation that the solution varies slowly in time. When evaluating the coefficients of the exponential time differencing and the exponential time differencing Runge Kutta methods via the”Cauchy integral”. All computational work is done with Matlab package.

References

10 Cites in Article

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CrossRef DOI
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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. "Fourier Spectral Methods for Numerical Solving of the Kuramoto-Sivashinsky Equation". Global Journal of Research in Engineering - I: Numerical Methods GJRE-I Volume 14 (GJRE Volume 14 Issue 18 (I1)).

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GJRE Volume 14 Issue 18 (I1)

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Journal Specifications

Crossref Journal DOI 10.17406/gjre

Print ISSN 0975-5861

e-ISSN 2249-4596

Keywords

cauchy integral discrete fourier transform exponential time differencing exponential time differencing runge kutta methods kuramoto-sivashinsky eq

Classification

GJRE-I Classification FOR Code: 010106

230116

Submission ReceivedDecember 14, 2013
Peer Review Double Blind
Handling Editor
Accepted January 1, 2014
Published May 19, 2014

Version of record

v1.2

Issue date

May 19, 2014

Language

English

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Article Matrices

Total Score: 101

Country: Albania

Subject: Global Journal of Research in Engineering - I: Numerical Methods

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

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Publish Date: 2014 05, Wed

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