On the Stable Difference Schemes for the Schrödinger Equation with Time Delay

In the present paper, the first and second order of accuracy difference schemes for the approximate solutions of the initial value problem for Schrödinger equation with time delay in a Hilbert space are presented. The theorem on stability estimates for the solutions of these difference schemes is established. The application of theorems on stability of difference schemes for the approximate solutions of the initial boundary value problems for Schrödinger partial differential equation is provided. Additionally, some illustrative numerical results are presented. © 2019 Walter de Gruyter GmbH, Berlin/Boston 2019.

Authors
Ashyralyev A. 1, 2 , Agirseven D.3
Journal
Computational Methods in Applied Mathematics
Publisher
Walter de Gruyter GmbH
Language
English
Status
Published
Link
External link
DOI
10.1515/cmam-2018-0107
Year
2019
Organizations
  • 1 Department of Mathematics, Near East University, Peoples Friendship University Russia, Ul Miklukho Maklaya 6, Moscow, 117198, Russian Federation
  • 2 Institute of Mathematics and Mathematical Modeling, Almaty-Kazakhstan, Mersin, 050010, Turkey
  • 3 Department of Mathematics, Trakya University, Edirne, 22030, Turkey
Keywords
Difference Schemes; Schrödinger Differential Equations; Stability Estimates
Date of creation
19.07.2019
Date of change
19.07.2019
Short link
https://repository.rudn.ru/en/records/article/record/39076/
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