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 es...

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Vydáno v:Journal of computational methods in applied mathematics Ročník 20; číslo 1; s. 27 - 38
Hlavní autoři: Ashyralyev, Allaberen, Agirseven, Deniz
Médium: Journal Article
Jazyk:angličtina
Vydáno: Minsk De Gruyter 01.01.2020
Walter de Gruyter GmbH
Témata:
35R10
65N06
Boundary value problems
Difference Schemes
Hilbert space
Partial differential equations
Schrodinger equation
Schrödinger Differential Equations
Stability
Stability Estimates
Theorems
Time lag
ISSN:1609-4840, 1609-9389
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Popis
Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1609-4840
1609-9389
DOI:10.1515/cmam-2018-0107