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 › Article › peer-review

19 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

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10.1080/01630563.2015.1065887

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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.",

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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.

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KW - Fractional Caputo derivative

KW - Maximum principle

KW - Regularity of solutions

KW - Time-fractional diffusion equation

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

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