gL1 scheme for solving a class of generalized time-fractional diffusion equations

In this paper, a numerical scheme based on a general temporal mesh is constructed for a generalized time-fractional diffusion problem of order α. The main idea involves the generalized linear interpolation and so we term the numerical scheme the gL1 scheme. The stability and convergence of the numer...

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Main Authors: Li, Xuhao, Wong, Patricia Jia Ying
Other Authors: School of Electrical and Electronic Engineering
Format: Article
Language:English
Published: 2022
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Online Access:https://hdl.handle.net/10356/160835
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1608352022-08-03T06:20:26Z gL1 scheme for solving a class of generalized time-fractional diffusion equations Li, Xuhao Wong, Patricia Jia Ying School of Electrical and Electronic Engineering Engineering::Electrical and electronic engineering Generalized Fractional Derivative Time-Diffusion Problem In this paper, a numerical scheme based on a general temporal mesh is constructed for a generalized time-fractional diffusion problem of order α. The main idea involves the generalized linear interpolation and so we term the numerical scheme the gL1 scheme. The stability and convergence of the numerical scheme are analyzed using the energy method. It is proven that the temporal convergence order is (2 − α) for a general temporal mesh. Simulation is carried out to verify the efficiency of the proposed numerical scheme. Published version 2022-08-03T06:20:26Z 2022-08-03T06:20:26Z 2022 Journal Article Li, X. & Wong, P. J. Y. (2022). gL1 scheme for solving a class of generalized time-fractional diffusion equations. Mathematics, 10(8), 1219-. https://dx.doi.org/10.3390/math10081219 2227-7390 https://hdl.handle.net/10356/160835 10.3390/math10081219 2-s2.0-85128742152 8 10 1219 en Mathematics © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Engineering::Electrical and electronic engineering
Generalized Fractional Derivative
Time-Diffusion Problem
spellingShingle Engineering::Electrical and electronic engineering
Generalized Fractional Derivative
Time-Diffusion Problem
Li, Xuhao
Wong, Patricia Jia Ying
gL1 scheme for solving a class of generalized time-fractional diffusion equations
description In this paper, a numerical scheme based on a general temporal mesh is constructed for a generalized time-fractional diffusion problem of order α. The main idea involves the generalized linear interpolation and so we term the numerical scheme the gL1 scheme. The stability and convergence of the numerical scheme are analyzed using the energy method. It is proven that the temporal convergence order is (2 − α) for a general temporal mesh. Simulation is carried out to verify the efficiency of the proposed numerical scheme.
author2 School of Electrical and Electronic Engineering
author_facet School of Electrical and Electronic Engineering
Li, Xuhao
Wong, Patricia Jia Ying
format Article
author Li, Xuhao
Wong, Patricia Jia Ying
author_sort Li, Xuhao
title gL1 scheme for solving a class of generalized time-fractional diffusion equations
title_short gL1 scheme for solving a class of generalized time-fractional diffusion equations
title_full gL1 scheme for solving a class of generalized time-fractional diffusion equations
title_fullStr gL1 scheme for solving a class of generalized time-fractional diffusion equations
title_full_unstemmed gL1 scheme for solving a class of generalized time-fractional diffusion equations
title_sort gl1 scheme for solving a class of generalized time-fractional diffusion equations
publishDate 2022
url https://hdl.handle.net/10356/160835
_version_ 1743119498719789056