On the convergence of difference schemes of high accuracy for the equation of ion-acoustic waves in a magnetized plasma
Multiparametric difference schemes of the finite element method of a high order of accuracy for the Sobolevtype equation of the fourth-order in time are studied. In particular, the first boundary value problem for the equation of ion-acoustic waves in a magnetized plasma is considered. A high-order...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2022-12-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Subjects: | |
| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/520 |
| _version_ | 1797372695536467968 |
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| author | M.M. Aripov D. Utebaev Zh.A. Nurullaev |
| author_facet | M.M. Aripov D. Utebaev Zh.A. Nurullaev |
| author_sort | M.M. Aripov |
| collection | DOAJ |
| description |
Multiparametric difference schemes of the finite element method of a high order of accuracy for the Sobolevtype equation of the fourth-order in time are studied. In particular, the first boundary value problem for the equation of ion-acoustic waves in a magnetized plasma is considered. A high-order accuracy of the scheme is achieved due to the special discretization of time and space variables. The presence of parameters in the scheme makes it possible to regularize the accuracy of the schemes and optimize the implementation
algorithm. An a priori estimate in a weak norm is obtained by the method of energy inequality. Based on this estimate and the Bramble-Hilbert lemma, the convergence of the constructed algorithms in classes of generalized solutions is proved. An algorithm for implementing the difference scheme is proposed.
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| first_indexed | 2024-03-08T18:38:35Z |
| format | Article |
| id | doaj.art-0645138a913c460fb873e5050a6e990f |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:38:35Z |
| publishDate | 2022-12-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-0645138a913c460fb873e5050a6e990f2023-12-29T10:19:13ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112022-12-01108410.31489/2022m4/4-19On the convergence of difference schemes of high accuracy for the equation of ion-acoustic waves in a magnetized plasmaM.M. AripovD. UtebaevZh.A. Nurullaev Multiparametric difference schemes of the finite element method of a high order of accuracy for the Sobolevtype equation of the fourth-order in time are studied. In particular, the first boundary value problem for the equation of ion-acoustic waves in a magnetized plasma is considered. A high-order accuracy of the scheme is achieved due to the special discretization of time and space variables. The presence of parameters in the scheme makes it possible to regularize the accuracy of the schemes and optimize the implementation algorithm. An a priori estimate in a weak norm is obtained by the method of energy inequality. Based on this estimate and the Bramble-Hilbert lemma, the convergence of the constructed algorithms in classes of generalized solutions is proved. An algorithm for implementing the difference scheme is proposed. http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/520Sobolev type equationdifference schemesfinite difference methodfinite element methodstabilityconvergence |
| spellingShingle | M.M. Aripov D. Utebaev Zh.A. Nurullaev On the convergence of difference schemes of high accuracy for the equation of ion-acoustic waves in a magnetized plasma Қарағанды университетінің хабаршысы. Математика сериясы Sobolev type equation difference schemes finite difference method finite element method stability convergence |
| title | On the convergence of difference schemes of high accuracy for the equation of ion-acoustic waves in a magnetized plasma |
| title_full | On the convergence of difference schemes of high accuracy for the equation of ion-acoustic waves in a magnetized plasma |
| title_fullStr | On the convergence of difference schemes of high accuracy for the equation of ion-acoustic waves in a magnetized plasma |
| title_full_unstemmed | On the convergence of difference schemes of high accuracy for the equation of ion-acoustic waves in a magnetized plasma |
| title_short | On the convergence of difference schemes of high accuracy for the equation of ion-acoustic waves in a magnetized plasma |
| title_sort | on the convergence of difference schemes of high accuracy for the equation of ion acoustic waves in a magnetized plasma |
| topic | Sobolev type equation difference schemes finite difference method finite element method stability convergence |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/520 |
| work_keys_str_mv | AT mmaripov ontheconvergenceofdifferenceschemesofhighaccuracyfortheequationofionacousticwavesinamagnetizedplasma AT dutebaev ontheconvergenceofdifferenceschemesofhighaccuracyfortheequationofionacousticwavesinamagnetizedplasma AT zhanurullaev ontheconvergenceofdifferenceschemesofhighaccuracyfortheequationofionacousticwavesinamagnetizedplasma |