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

Abdelhamid BeziaBen Mabrouk Anouar

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 (Ben Mabrouk Anouar)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-31-193, author = {Bezia , Abdelhamid and Anouar , Ben Mabrouk}, 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} }
TY - JOUR T1 - Finite Difference Method for (2+1)-Kuramoto-Sivashinsky Equation AU - Bezia , Abdelhamid AU - Anouar , Ben Mabrouk JO - Journal of Partial Differential Equations VL - 3 SP - 193 EP - 213 PY - 2018 DA - 2018/09 SN - 31 DO - http://doi.org/10.4208/jpde.v31.n3.1 UR - https://global-sci.org/intro/article_detail/jpde/12703.html KW - Kuramoto-Sivashinsky equation KW - Finite difference method KW - Lyapunov-Sylvester operators. AB -

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.

Abdelhamid Bezia & Ben Mabrouk Anouar. (2019). Finite Difference Method for (2+1)-Kuramoto-Sivashinsky Equation. Journal of Partial Differential Equations. 31 (3). 193-213. doi:10.4208/jpde.v31.n3.1
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