The Maximum Principle for Time-Fractional Diffusion Equations and Its Application

Hermann Brunner; Houde Han; Dongsheng Yin

doi:10.1080/01630563.2015.1065887

The Maximum Principle for Time-Fractional Diffusion Equations and Its Application

Hermann Brunner^*, Houde Han, Dongsheng Yin

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

24 Citations (Scopus)

Abstract

Using an equivalent reformulation of the definition of the Caputo fractional derivative, we present the stability and convergence analysis for a finite difference scheme that we use to solve a time-fractional diffusion equation. The analysis is based on a maximum principle for such equations.

Original language	English
Pages (from-to)	1307-1321
Number of pages	15
Journal	Numerical Functional Analysis and Optimization
Volume	36
Issue number	10
DOIs	https://doi.org/10.1080/01630563.2015.1065887
Publication status	Published - 3 Oct 2015

Scopus Subject Areas

Analysis
Signal Processing
Computer Science Applications
Control and Optimization

User-Defined Keywords

Finite difference schemes
Fractional Caputo derivative
Maximum principle
Regularity of solutions
Time-fractional diffusion equation

Access to Document

10.1080/01630563.2015.1065887

Cite this

@article{2309cb3e7ccb4078be48a5bc50acb82a,

title = "The Maximum Principle for Time-Fractional Diffusion Equations and Its Application",

abstract = "Using an equivalent reformulation of the definition of the Caputo fractional derivative, we present the stability and convergence analysis for a finite difference scheme that we use to solve a time-fractional diffusion equation. The analysis is based on a maximum principle for such equations.",

keywords = "Finite difference schemes, Fractional Caputo derivative, Maximum principle, Regularity of solutions, Time-fractional diffusion equation",

author = "Hermann Brunner and Houde Han and Dongsheng Yin",

note = "Funding Information: This research was supported by the Hong Kong Research Grants Council (RGC Grant No. HKBU 200210) and the Natural Sciences and Engineering Research Council of Canada (Discovery Grant No. 9406). H. Han was supported by National Science Foundation of China (Grant No. 11371218 and No. 91330203). D. Yin was supported by National Science Foundation of China (Grant No. 10901091 and No. 60873252) and The Importation and Development of High-Caliber Talents Project of Beijing Municipal Institutions.",

year = "2015",

month = oct,

day = "3",

doi = "10.1080/01630563.2015.1065887",

language = "English",

volume = "36",

pages = "1307--1321",

journal = "Numerical Functional Analysis and Optimization",

issn = "0163-0563",

publisher = "Taylor and Francis",

number = "10",

}

TY - JOUR

T1 - The Maximum Principle for Time-Fractional Diffusion Equations and Its Application

AU - Brunner, Hermann

AU - Han, Houde

AU - Yin, Dongsheng

N1 - Funding Information: This research was supported by the Hong Kong Research Grants Council (RGC Grant No. HKBU 200210) and the Natural Sciences and Engineering Research Council of Canada (Discovery Grant No. 9406). H. Han was supported by National Science Foundation of China (Grant No. 11371218 and No. 91330203). D. Yin was supported by National Science Foundation of China (Grant No. 10901091 and No. 60873252) and The Importation and Development of High-Caliber Talents Project of Beijing Municipal Institutions.

PY - 2015/10/3

Y1 - 2015/10/3

N2 - Using an equivalent reformulation of the definition of the Caputo fractional derivative, we present the stability and convergence analysis for a finite difference scheme that we use to solve a time-fractional diffusion equation. The analysis is based on a maximum principle for such equations.

AB - Using an equivalent reformulation of the definition of the Caputo fractional derivative, we present the stability and convergence analysis for a finite difference scheme that we use to solve a time-fractional diffusion equation. The analysis is based on a maximum principle for such equations.

KW - Finite difference schemes

KW - Fractional Caputo derivative

KW - Maximum principle

KW - Regularity of solutions

KW - Time-fractional diffusion equation

UR - http://www.scopus.com/inward/record.url?scp=84942884375&partnerID=8YFLogxK

U2 - 10.1080/01630563.2015.1065887

DO - 10.1080/01630563.2015.1065887

M3 - Journal article

AN - SCOPUS:84942884375

SN - 0163-0563

VL - 36

SP - 1307

EP - 1321

JO - Numerical Functional Analysis and Optimization

JF - Numerical Functional Analysis and Optimization

IS - 10

ER -

The Maximum Principle for Time-Fractional Diffusion Equations and Its Application

Abstract

Scopus Subject Areas

User-Defined Keywords

Access to Document

Other files and links

Fingerprint

Cite this