A fast solution method for time dependent multidimensional Schrödinger equations

In this paper we propose fast solution methods for the Cauchy problem for the multidimensional Schrödinger equation. Our approach is based on the approximation of the data by the basis functions introduced in the theory of approximate approximations. We obtain high-order approximations also in higher dimensions up to a small saturation error, which is negligible in computations, and we prove error estimates in mixed Lebesgue spaces for the inhomogeneous equation. The proposed method is very efficient in high dimensions if the densities allow separated representations. We illustrate the efficiency of the procedure on different examples, up to approximation order 6 and space dimension 200. © 2017 Informa UK Limited, trading as Taylor & Francis Group

Авторы
Lanzara F.1 , Maz’ya V. 2, 3 , Schmidt G.4
Журнал
Язык
Английский
Страницы
1-22
Статус
Опубликовано
Год
2017
Организации
  • 1 Department of Mathematics, Sapienza University, Rome, Italy
  • 2 S.M. Nikol‘skii Institute of Mathematics, RUDN University, Moscow, Russia
  • 3 Department of Mathematics, University of Linköping, Linköping, Sweden
  • 4 Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
Ключевые слова
error estimates; higher dimensions; Schrödinger equation; separated representations
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/5388/