Numerical Methods for Semilinear Fractional Diffusion Equations with Time Delay

Shuiping Yang; Yubin Liu; Hongyu Liu; Chao Wang

doi:10.4208/aamm.OA-2020-0387

Numerical Methods for Semilinear Fractional Diffusion Equations with Time Delay

Shuiping Yang, Yubin Liu, Hongyu Liu^*, Chao Wang^*

^*Corresponding author for this work

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

14 Citations (Scopus)

Abstract

In this paper, we consider the numerical solutions of the semilinear Riesz space-fractional diffusion equations (RSFDEs) with time delay, which constitute an important class of differential equations of practical significance. We develop a novel implicit alternating direction method that can effectively and efficiently tackle the RSFDEs in both two and three dimensions. The numerical method is proved to be uniquely solvable, stable and convergent with second order accuracy in both space and time. Numerical results are presented to verify the accuracy and efficiency of the proposed numerical scheme.

Original language	English
Pages (from-to)	56-78
Journal	Advances in Applied Mathematics and Mechanics
Volume	14
Issue number	1
Online published	Nov 2021
DOIs	https://doi.org/10.4208/aamm.OA-2020-0387
Publication status	Published - Feb 2022

Research Keywords

Semilinear Riesz space fractional diffusion equations with time delay
implicit alter-nating direction method
stability and convergence
DIFFERENTIAL-EQUATIONS
POLYHEDRAL SCATTERERS
SPECTRAL METHOD
ELEMENT-METHOD
SOUND-HARD
STABILITY
CONVERGENCE
UNIQUENESS
OBSTACLE
PRINCIPLE

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RGC-funded

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10.4208/aamm.OA-2020-0387

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@article{9b325c737cfb4971a42d95da42674f58,

title = "Numerical Methods for Semilinear Fractional Diffusion Equations with Time Delay",

abstract = "In this paper, we consider the numerical solutions of the semilinear Riesz space-fractional diffusion equations (RSFDEs) with time delay, which constitute an important class of differential equations of practical significance. We develop a novel implicit alternating direction method that can effectively and efficiently tackle the RSFDEs in both two and three dimensions. The numerical method is proved to be uniquely solvable, stable and convergent with second order accuracy in both space and time. Numerical results are presented to verify the accuracy and efficiency of the proposed numerical scheme.",

keywords = "Semilinear Riesz space fractional diffusion equations with time delay, implicit alter-nating direction method, stability and convergence, DIFFERENTIAL-EQUATIONS, POLYHEDRAL SCATTERERS, SPECTRAL METHOD, ELEMENT-METHOD, SOUND-HARD, STABILITY, CONVERGENCE, UNIQUENESS, OBSTACLE, PRINCIPLE",

author = "Shuiping Yang and Yubin Liu and Hongyu Liu and Chao Wang",

year = "2022",

month = feb,

doi = "10.4208/aamm.OA-2020-0387",

language = "English",

volume = "14",

pages = "56--78",

journal = "Advances in Applied Mathematics and Mechanics",

issn = "2070-0733",

publisher = "Cambridge University Press",

number = "1",

}

TY - JOUR

T1 - Numerical Methods for Semilinear Fractional Diffusion Equations with Time Delay

AU - Yang, Shuiping

AU - Liu, Yubin

AU - Liu, Hongyu

AU - Wang, Chao

PY - 2022/2

Y1 - 2022/2

N2 - In this paper, we consider the numerical solutions of the semilinear Riesz space-fractional diffusion equations (RSFDEs) with time delay, which constitute an important class of differential equations of practical significance. We develop a novel implicit alternating direction method that can effectively and efficiently tackle the RSFDEs in both two and three dimensions. The numerical method is proved to be uniquely solvable, stable and convergent with second order accuracy in both space and time. Numerical results are presented to verify the accuracy and efficiency of the proposed numerical scheme.

AB - In this paper, we consider the numerical solutions of the semilinear Riesz space-fractional diffusion equations (RSFDEs) with time delay, which constitute an important class of differential equations of practical significance. We develop a novel implicit alternating direction method that can effectively and efficiently tackle the RSFDEs in both two and three dimensions. The numerical method is proved to be uniquely solvable, stable and convergent with second order accuracy in both space and time. Numerical results are presented to verify the accuracy and efficiency of the proposed numerical scheme.

KW - Semilinear Riesz space fractional diffusion equations with time delay

KW - implicit alter-nating direction method

KW - stability and convergence

KW - DIFFERENTIAL-EQUATIONS

KW - POLYHEDRAL SCATTERERS

KW - SPECTRAL METHOD

KW - ELEMENT-METHOD

KW - SOUND-HARD

KW - STABILITY

KW - CONVERGENCE

KW - UNIQUENESS

KW - OBSTACLE

KW - PRINCIPLE

UR - http://www.scopus.com/inward/record.url?scp=85120614220&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85120614220&origin=recordpage

U2 - 10.4208/aamm.OA-2020-0387

DO - 10.4208/aamm.OA-2020-0387

M3 - RGC 21 - Publication in refereed journal

SN - 2070-0733

VL - 14

SP - 56

EP - 78

JO - Advances in Applied Mathematics and Mechanics

JF - Advances in Applied Mathematics and Mechanics

IS - 1

ER -

Numerical Methods for Semilinear Fractional Diffusion Equations with Time Delay

Abstract

Research Keywords

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GRF: Geometric Properties of Three Classes of Spectral Problems with Applications to Inverse Problems and Material Sciences

GRF: Mathematical and Computational Studies of Geomagnetic Anomaly Detections

GRF: Mathematical Analysis on Scattering from Corner Singularities, Inverse Shape Problems and Geometric Structures of Transmission Eigenfunctions

Cite this

Numerical Methods for Semilinear Fractional Diffusion Equations with Time Delay

Abstract

Research Keywords

RGC Funding Information

Access Output

Other Access Options

Permanent Link

Other Files and Links

Fingerprint

Projects

GRF: Geometric Properties of Three Classes of Spectral Problems with Applications to Inverse Problems and Material Sciences

GRF: Mathematical and Computational Studies of Geomagnetic Anomaly Detections

GRF: Mathematical Analysis on Scattering from Corner Singularities, Inverse Shape Problems and Geometric Structures of Transmission Eigenfunctions

Cite this