A note on solving the fourth-order Kuramoto-Sivashinsky equation by the compact finite difference scheme

The present article is concerned with the implementation of the compact finite difference scheme, in the space and the optimal four-stage, order three strong stability-preserving time-stepping Runge-Kutta (SSP-RK43) scheme, in time for computation of one dimensional Kuramoto-Sivashinsky equation (KS...

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Bibliographic Details
Published inAin Shams Engineering Journal Vol. 9; no. 4; pp. 1581 - 1589
Main Authors Singh, Brajesh Kumar, Arora, Geeta, Kumar, Pramod
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2018
Elsevier
Subjects
Compact finite difference scheme
Kuramoto-Sivashinsky equation
SSP-RK43 scheme
Thomas algorithm
SSP-RK43 scheme
Kuramoto-Sivashinsky equation
Thomas algorithm
Compact finite difference scheme
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Summary:The present article is concerned with the implementation of the compact finite difference scheme, in the space and the optimal four-stage, order three strong stability-preserving time-stepping Runge-Kutta (SSP-RK43) scheme, in time for computation of one dimensional Kuramoto-Sivashinsky equation (KSE), arises in the study of flame front propagation, phase turbulence in reaction-diffusion system and in many other biological and chemical processes. The efficiency of proposed scheme is confirmed by six test problems with known exact solutions. The numerical results demonstrate the reliability and efficiency of the algorithm developed.
ISSN:2090-4479
DOI:10.1016/j.asej.2016.11.008