Difference schemes for the numerical solution of the heat conduction equation with aftereffect / Pimenov V. G.,Lozhnikov A. B. // PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS. - 2011. - V. 275, l. 1. - P. 137-148.

ISSN/EISSN:

0081-5438 / нет данных

Type:

Article

Abstract:

A family of grid methods is constructed for the numerical solution of the heat conduction equation in the general form with delay; the methods are based on the idea of separating the current state and the prehistory function. A theorem is obtained on the order of convergence of the methods, which uses the technique of proving similar statements for functional differential equations and methods from the general theory of difference schemes. Results of calculating test examples with constant and variable delay are presented.

Author keywords:

numerical methods; heat conduction equation; delay; difference schemes; interpolation; extrapolation; order of convergence

DOI:

10.1134/S0081543811090100

Web of Science ID:

ISI:000297915900010

Соавторы в МНС:

Другие поля

Поле	Значение
Month	DEC
Publisher	MAIK NAUKA/INTERPERIODICA/SPRINGER
Address	233 SPRING ST, NEW YORK, NY 10013-1578 USA
Language	English
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics, Applied; Mathematics
Author-Email	Vladimir.Pimenov@usu.ru ABLozhnikov@yandex.ru
ResearcherID-Numbers	Pimenov, Vladimir/N-9894-2017
ORCID-Numbers	Pimenov, Vladimir/0000-0002-4042-6079
Funding-Acknowledgement	Russian Foundation for Basic Research {[}08-01-00141, 10-01-00377]; Presidium of the Russian Academy of Sciences
Funding-Text	This work was supported by the Russian Foundation for Basic Research (project nos. 08-01-00141 and 10-01-00377) and by the Program of the Presidium of the Russian Academy of Sciences ``Mathematical Theory of Control.{''}
Number-of-Cited-References	9
Usage-Count-Last-180-days	6
Usage-Count-Since-2013	41
Journal-ISO	Proc. Steklov Inst. Math.
Doc-Delivery-Number	859ZY