On the Stable Difference Schemes for the Schrödinger Equation with Time Delay-Reference-Cited by-同舟云学术

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

Published:2019-02-15 Issue:1 Volume:20 Page:27-38
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Ashyralyev Allaberen¹,Agirseven Deniz²

Affiliation:

1. Department of Mathematics , Near East University , Mersin 10 , Turkey ; and Peoples Friendship University Russia, Ul Miklukho Maklaya 6, Moscow 117198, Russia; and Institute of Mathematics and Mathematical Modeling, 050010, Almaty, Kazakhstan

2. Department of Mathematics , Trakya University , 22030 Edirne , Turkey

Abstract

Abstract 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.

Funder

Ministry of Education and Science of the Russian Federation

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

Link

https://www.degruyter.com/document/doi/10.1515/cmam-2018-0107/pdf

Reference39 articles.

1. D. Agirseven, On the stability of the Schrödinger equation with time delay, Filomat 32 (2018), no. 3, 759–766.

2. X. Antoine, C. Besse and V. Mouysset, Numerical schemes for the simulation of the two-dimensional Schrödinger equation using non-reflecting boundary conditions, Math. Comp. 73 (2004), no. 248, 1779–1799.

3. A. Ashyralyev and D. Agirseven, On convergence of difference schemes for delay parabolic equations, Comput. Math. Appl. 66 (2013), no. 7, 1232–1244.

4. A. Ashyralyev and D. Agirseven, Bounded solutions of nonlinear hyperbolic equations with time delay, Electron. J. Differential Equations 2018 (2018), Paper No. 21.

5. A. Ashyralyev and B. Hicdurmaz, A note on the fractional Schrödinger differential equations, Kybernetes 40 (2011), no. 5–6, 736–750.

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