Two-level schemes of Cauchy problem method for solving fractional powers of elliptic operators

In this paper we develop and investigate numerical algorithms for solving equations of the first order for the fractional powers of discrete elliptic operators: Aαy=φ, 0<α<1, for φ∈Vh with Vh a finite element or discrete approximation space. The main goal is to consider two different approaches to construct efficient high order time stepping schemes for the implementation of the Cauchy problem method (Vabishchevich, 2015). The first approach is based on a solution of the related time-dependent PDE, and the second approach is based on diagonal Padé approximations to (1+x)−α when the relation of the solution on two times levels is used. The second and fourth order approximations are constructed by both approaches. In order to increase the accuracy of approximations the graded time grid is constructed which compensates the singular behavior of the solution for t close to 0. Results of numerical experiments are presented, they agree well with the theoretical results. © 2019 Elsevier Ltd

Авторы
Čiegis R.1 , Vabishchevich P.N. 2, 3
Редакторы
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Издательство
Elsevier Ltd
Номер выпуска
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Язык
Английский
Страницы
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Статус
Опубликовано
Подразделение
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Номер
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Том
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Год
2019
Организации
  • 1 Vilnius Gediminas Technical University, Sauletekio al. 11, Vilnius, 10223, Lithuania
  • 2 Nuclear Safety Institute, Russian Academy of Sciences, 52, B. Tulskaya, Moscow, Russian Federation
  • 3 Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, Russian Federation
Ключевые слова
Elliptic operator; Finite element approximation; Fractional power of an operator; Stability of difference schemes; Two-level schemes
Дата создания
24.12.2019
Дата изменения
24.12.2019
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/55504/