Dissipative Structures of the Kuramoto–Sivashinsky Equation
In the present work, we study the features of dissipative structures formation described by the periodic boundary value problem for the Kuramoto-Sivashinsky equation. The numerical algorithm which is based on the pseudospectral method is presented. We prove the efficiency and accuracy of the propose...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2015-02-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/234 |
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| author | N. A. Kudryashov P. N. Ryabov B. A. Petrov |
| author_facet | N. A. Kudryashov P. N. Ryabov B. A. Petrov |
| author_sort | N. A. Kudryashov |
| collection | DOAJ |
| description | In the present work, we study the features of dissipative structures formation described by the periodic boundary value problem for the Kuramoto-Sivashinsky equation. The numerical algorithm which is based on the pseudospectral method is presented. We prove the efficiency and accuracy of the proposed numerical method on the exact solution of the equation considered. Using this approach, we performed the numerical simulation of dissipative structure formations described by the Kuramoto–Sivashinsky equation. The influence of the problem parameters on these processes are studied. The quantitative and qualitative characteristics of dissipative structure formations are described. We have shown that there is a value of the control parameter at which the processes of dissipative structure formation are observed. In particular, using the cyclic convolution we define the average value of this parameter. Also, we find the dependence of the amplitude of the structures on the value of control parameter. |
| format | Article |
| id | doaj-art-021f2a0e47ce462e98a3625f5245f03a |
| institution | Kabale University |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2015-02-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-021f2a0e47ce462e98a3625f5245f03a2025-08-20T03:44:18ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172015-02-0122110511310.18255/1818-1015-2015-1-105-113227Dissipative Structures of the Kuramoto–Sivashinsky EquationN. A. Kudryashov0P. N. Ryabov1B. A. Petrov2National Research Nuclear University MEPhINational Research Nuclear University MEPhINational Research Nuclear University MEPhIIn the present work, we study the features of dissipative structures formation described by the periodic boundary value problem for the Kuramoto-Sivashinsky equation. The numerical algorithm which is based on the pseudospectral method is presented. We prove the efficiency and accuracy of the proposed numerical method on the exact solution of the equation considered. Using this approach, we performed the numerical simulation of dissipative structure formations described by the Kuramoto–Sivashinsky equation. The influence of the problem parameters on these processes are studied. The quantitative and qualitative characteristics of dissipative structure formations are described. We have shown that there is a value of the control parameter at which the processes of dissipative structure formation are observed. In particular, using the cyclic convolution we define the average value of this parameter. Also, we find the dependence of the amplitude of the structures on the value of control parameter.https://www.mais-journal.ru/jour/article/view/234kuramoto–sivashinsky equationself–organizationpatternspseudospectral methodnumerical simulation |
| spellingShingle | N. A. Kudryashov P. N. Ryabov B. A. Petrov Dissipative Structures of the Kuramoto–Sivashinsky Equation Моделирование и анализ информационных систем kuramoto–sivashinsky equation self–organization patterns pseudospectral method numerical simulation |
| title | Dissipative Structures of the Kuramoto–Sivashinsky Equation |
| title_full | Dissipative Structures of the Kuramoto–Sivashinsky Equation |
| title_fullStr | Dissipative Structures of the Kuramoto–Sivashinsky Equation |
| title_full_unstemmed | Dissipative Structures of the Kuramoto–Sivashinsky Equation |
| title_short | Dissipative Structures of the Kuramoto–Sivashinsky Equation |
| title_sort | dissipative structures of the kuramoto sivashinsky equation |
| topic | kuramoto–sivashinsky equation self–organization patterns pseudospectral method numerical simulation |
| url | https://www.mais-journal.ru/jour/article/view/234 |
| work_keys_str_mv | AT nakudryashov dissipativestructuresofthekuramotosivashinskyequation AT pnryabov dissipativestructuresofthekuramotosivashinskyequation AT bapetrov dissipativestructuresofthekuramotosivashinskyequation |