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Treffer: An efficient computational scheme for solving coupled time-fractional Schrödinger equation via cubic B-spline functions.

Title:
An efficient computational scheme for solving coupled time-fractional Schrödinger equation via cubic B-spline functions.
Authors:
Mubashir Hayat A; Department of Mathematics, University of Sargodha, Sargodha, Pakistan., Abbas M; Department of Mathematics, University of Sargodha, Sargodha, Pakistan., Emadifar H; Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai, Tamil Nadu, India.; MEU Research Unit, Middle East University, Amman, Jordan.; Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran., Alzaidi ASM; Department of Mathematics and Statistics, College of Science, Taif University, Taif, Saudi Arabia., Nazir T; Department of Mathematics, University of Sargodha, Sargodha, Pakistan., Aini Abdullah F; School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia.
Source:
PloS one [PLoS One] 2024 May 16; Vol. 19 (5), pp. e0296909. Date of Electronic Publication: 2024 May 16 (Print Publication: 2024).
Publication Type:
Journal Article
Language:
English
Journal Info:
Publisher: Public Library of Science Country of Publication: United States NLM ID: 101285081 Publication Model: eCollection Cited Medium: Internet ISSN: 1932-6203 (Electronic) Linking ISSN: 19326203 NLM ISO Abbreviation: PLoS One Subsets: MEDLINE
Imprint Name(s):
Original Publication: San Francisco, CA : Public Library of Science
MeSH Terms:
Algorithms*, Models, Theoretical ; Quantum Theory ; Computer Simulation
References:
Chaos. 2019 Feb;29(2):023102. (PMID: 30823718)
Adv Differ Equ. 2020;2020(1):577. (PMID: 33082774)
Entry Date(s):
Date Created: 20240516 Date Completed: 20240516 Latest Revision: 20240518
Update Code:
20250114
PubMed Central ID:
PMC11098432
DOI:
10.1371/journal.pone.0296909
PMID:
38753667
Database:
MEDLINE

Weitere Informationen

The time fractional Schrödinger equation contributes to our understanding of complex quantum systems, anomalous diffusion processes, and the application of fractional calculus in physics and cubic B-spline is a versatile tool in numerical analysis and computer graphics. This paper introduces a numerical method for solving the time fractional Schrödinger equation using B-spline functions and the Atangana-Baleanu fractional derivative. The proposed method employs a finite difference scheme to discretize the fractional derivative in time, while a θ-weighted scheme is used to discretize the space directions. The efficiency of the method is demonstrated through numerical results, and error norms are examined at various values of the non-integer parameter, temporal directions, and spatial directions.
(Copyright: © 2024 Mubashir Hayat et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

The authors have declared that no competing interests exist.