{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T05:02:01Z","timestamp":1770008521530,"version":"3.49.0"},"reference-count":39,"publisher":"Walter de Gruyter GmbH","issue":"1","funder":[{"DOI":"10.13039\/501100003443","name":"Ministry of Education and Science of the Russian Federation","doi-asserted-by":"publisher","award":["02.A03.21.0008"],"award-info":[{"award-number":["02.A03.21.0008"]}],"id":[{"id":"10.13039\/501100003443","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In the present paper, the first and second order of accuracy difference schemes for the approximate solutions of the initial value problem for Schr\u00f6dinger 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 Schr\u00f6dinger partial differential equation is provided. Additionally, some illustrative numerical results are presented.<\/jats:p>","DOI":"10.1515\/cmam-2018-0107","type":"journal-article","created":{"date-parts":[[2019,2,15]],"date-time":"2019-02-15T09:03:43Z","timestamp":1550221423000},"page":"27-38","source":"Crossref","is-referenced-by-count":9,"title":["On the Stable Difference Schemes for the Schr\u00f6dinger Equation with Time Delay"],"prefix":"10.1515","volume":"20","author":[{"given":"Allaberen","family":"Ashyralyev","sequence":"first","affiliation":[{"name":"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"}]},{"given":"Deniz","family":"Agirseven","sequence":"additional","affiliation":[{"name":"Department of Mathematics , Trakya University , 22030 Edirne , Turkey"}]}],"member":"374","published-online":{"date-parts":[[2019,2,15]]},"reference":[{"key":"2023033110163512209_j_cmam-2018-0107_ref_001","doi-asserted-by":"crossref","unstructured":"D.  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