Asymptotic expansion of the error of the numerical method for solving wave equation with functional delay
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
Asymptotic expansion of the error of the numerical method for solving wave equation with functional delay
|
|
| Автор |
Pimenov, V. G.
Tashirova, E. E. |
|
| Тематика |
FUNCTIONAL DELAY
NUMERICAL METHOD WITH WEIGHTS ORDER OF CONVERGENCE PIECEWISE CUBIC INTERPOLATION RICHARDSON METHOD WAVE EQUATION |
|
| Описание |
A wave equation with functional delay is considered. The problem is discretized. Constructions of the difference method with weights with piecewise linear interpolation are given. A basic method with weights with piecewise cubic interpolation is constructed. The order of the residual is studied without interpolation of the basic method, and the expansion coefficients of the residual with respect to time-steps and space-steps are written out. It is proved that the weighted method with piecewise cubic interpolation converges with order 2 in the energy norm. An equation is written for the main term of the asymptotic expansion of the global error of the basic method. Under certain assumptions, the validity of the application of the Richardson extrapolation procedure is substantiated, and the corresponding numerical method is constructed, that has the fourth order of convergence with respect to time-steps and space-steps. The validity of Runge’s formulas for practical estimation of the error is proved. The results of numerical experiments on a test example are presented. © 2024 Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta. All rights reserved.
Russian Science Foundation, RSF: 22–21–00075 Funding. The study was supported by the Russian Science Foundation, project no. 22–21–00075. |
|
| Дата |
2024-04-05T16:39:14Z
2024-04-05T16:39:14Z 2023 |
|
| Тип |
Article
Journal article (info:eu-repo/semantics/article) |info:eu-repo/semantics/publishedVersion |
|
| Идентификатор |
Пименов, ВГ & Таширова, ЕЕ 2023, 'АСИМПТОТИЧЕСКОЕ РАЗЛОЖЕНИЕ ПОГРЕШНОСТИ ЧИСЛЕННОГО МЕТОДА ДЛЯ РЕШЕНИЯ ВОЛНОВОГО УРАВНЕНИЯ С ФУНКЦИОНАЛЬНЫМ ЗАПАЗДЫВАНИЕМ', Известия Института математики и информатики Удмуртского государственного университета, Том. 62, стр. 71-86. https://doi.org/10.35634/2226-3594-2023-62-06
Пименов, В. Г., & Таширова, Е. Е. (2023). АСИМПТОТИЧЕСКОЕ РАЗЛОЖЕНИЕ ПОГРЕШНОСТИ ЧИСЛЕННОГО МЕТОДА ДЛЯ РЕШЕНИЯ ВОЛНОВОГО УРАВНЕНИЯ С ФУНКЦИОНАЛЬНЫМ ЗАПАЗДЫВАНИЕМ. Известия Института математики и информатики Удмуртского государственного университета, 62, 71-86. https://doi.org/10.35634/2226-3594-2023-62-06 2226-3594 Final All Open Access, Bronze https://www.scopus.com/inward/record.uri?eid=2-s2.0-85183668557&doi=10.35634%2f2226-3594-2023-62-06&partnerID=40&md5=5026ae3faf58b5c87af626380a8e55a3 https://www.mathnet.ru/php/getFT.phtml?jrnid=iimi&paperid=454&what=fullt&option_lang=eng http://elar.urfu.ru/handle/10995/131133 54938926 10.35634/2226-3594-2023-62-06 85183668557 001163723700006 |
|
| Язык |
ru
|
|
| Связанные ресурсы |
info:eu-repo/grantAgreement/RSF//22-21-00075
|
|
| Права |
Open access (info:eu-repo/semantics/openAccess)
|
|
| Формат |
application/pdf
|
|
| Издатель |
Udmurt State University
|
|
| Источник |
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta |
|