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Efficient Computation of the Nonlinear Schrödinger Equation with Time-Dependent Coefficients

Athinoula A. Kosti Orcid Logo, Simon Colreavy-Donnelly Orcid Logo, Fabio Caraffini Orcid Logo, Zacharias A. Anastassi Orcid Logo

Mathematics, Volume: 8, Issue: 3, Start page: 374

Swansea University Author: Fabio Caraffini Orcid Logo

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DOI (Published version): 10.3390/math8030374

Abstract

Motivated by the limited work performed on the development of computational techniques for solving the nonlinear Schrödinger equation with time-dependent coefficients, we develop a modified Runge–Kutta pair with improved periodicity and stability characteristics. Additionally, we develop a modified...

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Published in: Mathematics
ISSN: 2227-7390
Published: MDPI AG 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa60956
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spelling 2022-09-21T14:48:10.5240244 v2 60956 2022-08-28 Efficient Computation of the Nonlinear Schrödinger Equation with Time-Dependent Coefficients d0b8d4e63d512d4d67a02a23dd20dfdb 0000-0001-9199-7368 Fabio Caraffini Fabio Caraffini true false 2022-08-28 SCS Motivated by the limited work performed on the development of computational techniques for solving the nonlinear Schrödinger equation with time-dependent coefficients, we develop a modified Runge–Kutta pair with improved periodicity and stability characteristics. Additionally, we develop a modified step size control algorithm, which increases the efficiency of our pair and all other pairs included in the numerical experiments. The numerical results on the nonlinear Schrödinger equation with a periodic solution verified the superiority of the new algorithm in terms of efficiency. The new method also presents a good behaviour of the maximum absolute error and the global norm in time, even after a high number of oscillations. Journal Article Mathematics 8 3 374 MDPI AG 2227-7390 nonlinear Schrödinger equation; periodic coefficients; varying dispersion; varying nonlinearity; Runge–Kutta pair; phase-lag; amplification error; step size control; local error estimation 7 3 2020 2020-03-07 10.3390/math8030374 COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University This research received no external funding. 2022-09-21T14:48:10.5240244 2022-08-28T20:45:54.0644967 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Athinoula A. Kosti 0000-0002-1634-1171 1 Simon Colreavy-Donnelly 0000-0002-1795-6995 2 Fabio Caraffini 0000-0001-9199-7368 3 Zacharias A. Anastassi 0000-0001-9190-2816 4 60956__25185__3669f6771f1741c5a2baae3a1828d42c.pdf 60956_VoR.pdf 2022-09-21T14:47:00.0369498 Output 1033828 application/pdf Version of Record true Copyright: 2020 by the authors. This is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license true eng http://creativecommons.org/licenses/by/4.0/
title Efficient Computation of the Nonlinear Schrödinger Equation with Time-Dependent Coefficients
spellingShingle Efficient Computation of the Nonlinear Schrödinger Equation with Time-Dependent Coefficients
Fabio Caraffini
title_short Efficient Computation of the Nonlinear Schrödinger Equation with Time-Dependent Coefficients
title_full Efficient Computation of the Nonlinear Schrödinger Equation with Time-Dependent Coefficients
title_fullStr Efficient Computation of the Nonlinear Schrödinger Equation with Time-Dependent Coefficients
title_full_unstemmed Efficient Computation of the Nonlinear Schrödinger Equation with Time-Dependent Coefficients
title_sort Efficient Computation of the Nonlinear Schrödinger Equation with Time-Dependent Coefficients
author_id_str_mv d0b8d4e63d512d4d67a02a23dd20dfdb
author_id_fullname_str_mv d0b8d4e63d512d4d67a02a23dd20dfdb_***_Fabio Caraffini
author Fabio Caraffini
author2 Athinoula A. Kosti
Simon Colreavy-Donnelly
Fabio Caraffini
Zacharias A. Anastassi
format Journal article
container_title Mathematics
container_volume 8
container_issue 3
container_start_page 374
publishDate 2020
institution Swansea University
issn 2227-7390
doi_str_mv 10.3390/math8030374
publisher MDPI AG
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Computer Science{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Computer Science
document_store_str 1
active_str 0
description Motivated by the limited work performed on the development of computational techniques for solving the nonlinear Schrödinger equation with time-dependent coefficients, we develop a modified Runge–Kutta pair with improved periodicity and stability characteristics. Additionally, we develop a modified step size control algorithm, which increases the efficiency of our pair and all other pairs included in the numerical experiments. The numerical results on the nonlinear Schrödinger equation with a periodic solution verified the superiority of the new algorithm in terms of efficiency. The new method also presents a good behaviour of the maximum absolute error and the global norm in time, even after a high number of oscillations.
published_date 2020-03-07T04:19:29Z
_version_ 1763754293149564928
score 11.016235

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