{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,20]],"date-time":"2025-12-20T22:19:22Z","timestamp":1766269162637,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,8,25]],"date-time":"2023-08-25T00:00:00Z","timestamp":1692921600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Xinjiang Uygur Autonomous","award":["2021D01C068"],"award-info":[{"award-number":["2021D01C068"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we first established a high-accuracy difference scheme for the time-fractional Schr\u00f6dinger equation (TFSE), where the factional term is described in the Caputo derivative. We used the L1-2-3 formula to approximate the Caputo derivative, and the fourth-order compact finite difference scheme is utilized for discretizing the spatial term. The unconditional stability and convergence of the scheme in the maximum norm are proved. Finally, we verified the theoretical result with a numerical test.<\/jats:p>","DOI":"10.3390\/axioms12090816","type":"journal-article","created":{"date-parts":[[2023,8,25]],"date-time":"2023-08-25T08:42:20Z","timestamp":1692952940000},"page":"816","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Numerical Solution of Time-Fractional Schr\u00f6dinger Equation by Using FDM"],"prefix":"10.3390","volume":"12","author":[{"given":"Moldir","family":"Serik","sequence":"first","affiliation":[{"name":"College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China"}]},{"given":"Rena","family":"Eskar","sequence":"additional","affiliation":[{"name":"College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2228-9111","authenticated-orcid":false,"given":"Pengzhan","family":"Huang","sequence":"additional","affiliation":[{"name":"College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.1103\/PhysRev.28.1049","article-title":"An undulatory theory of the mechanics of atoms and molecules","volume":"28","year":"1926","journal-title":"Phys. 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