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A finite difference method for the very weak solution to a Cauchy problem for an elliptic equation Научная публикация

Журнал Journal of Inverse and Ill-Posed Problems
ISSN: 0928-0219 , E-ISSN: 1569-3945
Вых. Данные Год: 2018, Том: 26, Номер: 6, Страницы: 835-857 Страниц : 23 DOI: 10.1515/jiip-2018-0060
Ключевые слова Cauchy problem; elliptic equation; finite difference scheme; ill-posed problems; non-local boundary value problems; regularization; very weak solution
Авторы Hào D.N. 1 , Thu Giang 2 , Kabanikhin S. 3,4,5 , Shishlenin M. 3,4,5
Организации
1 Hanoi Institute of Mathematics, VAST, 18 Hoang Quoc Viet Road, Hanoi, Viet Nam
2 Thuongmai University, Ho Tung Mau, Hanoi, Viet Nam
3 Institute of Computational Mathematics and Mathematical Geophysics, 6 Lavrentieva Prospect, Novosibirsk, Russian Federation
4 Sobolev Institute of Mathematics, 4 Koptyuga Prospect, Novosibirsk, Russian Federation
5 Novosibirsk State University, 1 Pirogova str., Novosibirsk, Russian Federation

Реферат: We introduce the concept of very weak solution to a Cauchy problem for elliptic equations. The Cauchy problem is regularized by a well-posed non-local boundary value problem whose solution is also understood in a very weak sense. A stable finite difference scheme is suggested for solving the non-local boundary value problem and then applied to stabilizing the Cauchy problem. Some numerical examples are presented for showing the efficiency of the method. © 2018 Walter de Gruyter GmbH, Berlin/Boston.
Библиографическая ссылка: Hào D.N. , Thu G. , Kabanikhin S. , Shishlenin M.
A finite difference method for the very weak solution to a Cauchy problem for an elliptic equation
Journal of Inverse and Ill-Posed Problems. 2018. V.26. N6. P.835-857. DOI: 10.1515/jiip-2018-0060 WOS Scopus OpenAlex
Идентификаторы БД:
Web of science: WOS:000451640900008
Scopus: 2-s2.0-85055007477
OpenAlex: W2897205603
Цитирование в БД:
БД Цитирований
Scopus 11
OpenAlex 12
Web of science 8
Альметрики: