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

  • Allaberen Ashyralyev and Deniz Agirseven EMAIL logo

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.

MSC 2010: 65N06; 35R10

Award Identifier / Grant number: 02.A03.21.0008

Funding statement: The publication has been prepared with the support of the “RUDN University Program 5-100” and published under target program BR05236656 of the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan.

Acknowledgements

We would like to thank the referees for their helpful suggestions to the improvement of our paper.

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Received: 2018-03-08
Revised: 2018-07-06
Accepted: 2019-01-19
Published Online: 2019-02-15
Published in Print: 2020-01-01

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