Quintic non-polynomial spline for time-fractional nonlinear Schrödinger equation
In this paper, we shall solve a time-fractional nonlinear Schrödinger equation by using the quintic non-polynomial spline and the L1 formula. The unconditional stability, unique solvability and convergence of our numerical scheme are proved by the Fourier method. It is shown that our method is sixth...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2021
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/148351 |
| _version_ | 1824454840858705920 |
|---|---|
| author | Ding, Qinxu Wong, Patricia Jia Yiing |
| author2 | School of Electrical and Electronic Engineering |
| author_facet | School of Electrical and Electronic Engineering Ding, Qinxu Wong, Patricia Jia Yiing |
| author_sort | Ding, Qinxu |
| collection | NTU |
| description | In this paper, we shall solve a time-fractional nonlinear Schrödinger equation by using the quintic non-polynomial spline and the L1 formula. The unconditional stability, unique solvability and convergence of our numerical scheme are proved by the Fourier method. It is shown that our method is sixth order accurate in the spatial dimension and (2-γ) th order accurate in the temporal dimension, where γ is the fractional order. The efficiency of the proposed numerical scheme is further illustrated by numerical experiments, meanwhile the simulation results indicate better performance over previous work in the literature. |
| first_indexed | 2025-02-19T03:28:43Z |
| format | Journal Article |
| id | ntu-10356/148351 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2025-02-19T03:28:43Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | ntu-10356/1483512021-04-29T08:31:06Z Quintic non-polynomial spline for time-fractional nonlinear Schrödinger equation Ding, Qinxu Wong, Patricia Jia Yiing School of Electrical and Electronic Engineering Engineering::Electrical and electronic engineering Quintic Non-polynomial Spline Time-fractional Derivative In this paper, we shall solve a time-fractional nonlinear Schrödinger equation by using the quintic non-polynomial spline and the L1 formula. The unconditional stability, unique solvability and convergence of our numerical scheme are proved by the Fourier method. It is shown that our method is sixth order accurate in the spatial dimension and (2-γ) th order accurate in the temporal dimension, where γ is the fractional order. The efficiency of the proposed numerical scheme is further illustrated by numerical experiments, meanwhile the simulation results indicate better performance over previous work in the literature. Published version 2021-04-29T08:31:06Z 2021-04-29T08:31:06Z 2020 Journal Article Ding, Q. & Wong, P. J. Y. (2020). Quintic non-polynomial spline for time-fractional nonlinear Schrödinger equation. Advances in Difference Equations, 2020(1). https://dx.doi.org/10.1186/s13662-020-03021-0 1687-1839 0000-0001-8375-5553 https://hdl.handle.net/10356/148351 10.1186/s13662-020-03021-0 33082774 2-s2.0-85092573017 1 2020 en Advances in Difference Equations © 2020 The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. application/pdf |
| spellingShingle | Engineering::Electrical and electronic engineering Quintic Non-polynomial Spline Time-fractional Derivative Ding, Qinxu Wong, Patricia Jia Yiing Quintic non-polynomial spline for time-fractional nonlinear Schrödinger equation |
| title | Quintic non-polynomial spline for time-fractional nonlinear Schrödinger equation |
| title_full | Quintic non-polynomial spline for time-fractional nonlinear Schrödinger equation |
| title_fullStr | Quintic non-polynomial spline for time-fractional nonlinear Schrödinger equation |
| title_full_unstemmed | Quintic non-polynomial spline for time-fractional nonlinear Schrödinger equation |
| title_short | Quintic non-polynomial spline for time-fractional nonlinear Schrödinger equation |
| title_sort | quintic non polynomial spline for time fractional nonlinear schrodinger equation |
| topic | Engineering::Electrical and electronic engineering Quintic Non-polynomial Spline Time-fractional Derivative |
| url | https://hdl.handle.net/10356/148351 |
| work_keys_str_mv | AT dingqinxu quinticnonpolynomialsplinefortimefractionalnonlinearschrodingerequation AT wongpatriciajiayiing quinticnonpolynomialsplinefortimefractionalnonlinearschrodingerequation |