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Highly accurate compact difference schemes for multidimensional delay Schrödinger equations

  • Allaberen Ashyralyev ORCID logo , Deniz Agirseven ORCID logo EMAIL logo and Baris Erköse
Published/Copyright: June 17, 2025
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Abstract

In present paper, the second-order accurate stable compact difference schemes (DSs) for the delay Schrödinger-type partial differential equation (DSPDE) in a Hilbert space are constructed. The stability of these DSs is established. As applications, stability estimates (SEs) for the solutions of DSs for two types of DSPDEs are derived. A numerical method is proposed for solving one and two-dimensional DSPDEs.

MSC 2020: 65M06; 65M12

Funding statement: The work was supported by the RUDN Program 5-100 and within the framework of the target program BR05236656 of the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan.

Acknowledgements

The authors express their gratitude to the reviewers for their useful advice on improving the article.

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Received: 2024-11-08
Revised: 2025-03-12
Accepted: 2025-03-19
Published Online: 2025-06-17

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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