Volume 31, Issue 3
Finite Difference Method for (2+1)-Kuramoto-Sivashinsky Equation

Abdelhamid Bezia & Anouar Ben Mabrouk

J. Part. Diff. Eq., 31 (2018), pp. 193-213.

Published online: 2018-09

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  • Abstract

This paper investigates a solution technique for solving a two-dimensional Kuramoto-Sivashinsky equation discretized using a finite difference method. It consists of an order reduction method into a coupled system of second-order equations, and to formulate the fully discretized, implicit time-marched system as a Lyapunov-Sylvester matrix equation. Convergence and stability is examined using Lyapunov criterion and manipulating generalized Lyapunov-Sylvester operators. Some numerical implementations are provided at the end to validate the theoretical results.

  • Keywords

Kuramoto-Sivashinsky equation Finite difference method Lyapunov-Sylvester operators.

  • AMS Subject Headings

65M06 65M12 65M22 15A30 37B25.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

abdelhamid.bezia@gmail.com (Abdelhamid Bezia)

anouar.benmabrouk@fsm.rnu.tn (Anouar Ben Mabrouk)

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@Article{JPDE-31-193, author = {Bezia , Abdelhamid and Mabrouk , Anouar Ben }, title = {Finite Difference Method for (2+1)-Kuramoto-Sivashinsky Equation}, journal = {Journal of Partial Differential Equations}, year = {2018}, volume = {31}, number = {3}, pages = {193--213}, abstract = {

This paper investigates a solution technique for solving a two-dimensional Kuramoto-Sivashinsky equation discretized using a finite difference method. It consists of an order reduction method into a coupled system of second-order equations, and to formulate the fully discretized, implicit time-marched system as a Lyapunov-Sylvester matrix equation. Convergence and stability is examined using Lyapunov criterion and manipulating generalized Lyapunov-Sylvester operators. Some numerical implementations are provided at the end to validate the theoretical results.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v31.n3.1}, url = {http://global-sci.org/intro/article_detail/jpde/12703.html} }
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