Numerical simulations of 2D fractional subdiffusion problems

Hermann Brunner; Leevan Ling; Masahiro Yamamoto

doi:10.1016/j.jcp.2010.05.015

Numerical simulations of 2D fractional subdiffusion problems

Hermann Brunner, Leevan Ling^*, Masahiro Yamamoto

^*Corresponding author for this work

Department of Mathematics

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

103 Citations (Scopus)

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Abstract

The growing number of applications of fractional derivatives in various fields of science and engineering indicates that there is a significant demand for better mathematical algorithms for models with real objects and processes. Currently, most algorithms are designed for 1D problems due to the memory effect in fractional derivatives. In this work, the 2D fractional subdiffusion problems are solved by an algorithm that couples an adaptive time stepping and adaptive spatial basis selection approach. The proposed algorithm is also used to simulate a subdiffusion-convection equation.

Original language	English
Pages (from-to)	6613-6622
Number of pages	10
Journal	Journal of Computational Physics
Volume	229
Issue number	18
Early online date	24 May 2010
DOIs	https://doi.org/10.1016/j.jcp.2010.05.015
Publication status	Published - Sept 2010

Scopus Subject Areas

Numerical Analysis
Modelling and Simulation
Physics and Astronomy (miscellaneous)
Physics and Astronomy(all)
Computer Science Applications
Computational Mathematics
Applied Mathematics

User-Defined Keywords

Fractional differential equations
Kansa’s method
Radial basis functions
Collocation
Adaptive greedy algorithm
Geometric time grids

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10.1016/j.jcp.2010.05.015

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title = "Numerical simulations of 2D fractional subdiffusion problems",

abstract = "The growing number of applications of fractional derivatives in various fields of science and engineering indicates that there is a significant demand for better mathematical algorithms for models with real objects and processes. Currently, most algorithms are designed for 1D problems due to the memory effect in fractional derivatives. In this work, the 2D fractional subdiffusion problems are solved by an algorithm that couples an adaptive time stepping and adaptive spatial basis selection approach. The proposed algorithm is also used to simulate a subdiffusion-convection equation.",

keywords = "Fractional differential equations, Kansa{\textquoteright}s method, Radial basis functions, Collocation, Adaptive greedy algorithm, Geometric time grids",

author = "Hermann Brunner and Leevan Ling and Masahiro Yamamoto",

note = "This project was supported by the CERG Grant of Hong Kong Research Grant Council and the FRG grant of Hong Kong Baptist University. This work has been mostly done during the stay of the second named author at the Graduate School of Mathematical Sciences of the University of Tokyo in December 2008–January 2009, and the stay was supported by Global COE Program “The Research and Training Center for New Development in Mathematics”.",

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doi = "10.1016/j.jcp.2010.05.015",

language = "English",

volume = "229",

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T1 - Numerical simulations of 2D fractional subdiffusion problems

AU - Brunner, Hermann

AU - Ling, Leevan

AU - Yamamoto, Masahiro

N1 - This project was supported by the CERG Grant of Hong Kong Research Grant Council and the FRG grant of Hong Kong Baptist University. This work has been mostly done during the stay of the second named author at the Graduate School of Mathematical Sciences of the University of Tokyo in December 2008–January 2009, and the stay was supported by Global COE Program “The Research and Training Center for New Development in Mathematics”.

PY - 2010/9

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N2 - The growing number of applications of fractional derivatives in various fields of science and engineering indicates that there is a significant demand for better mathematical algorithms for models with real objects and processes. Currently, most algorithms are designed for 1D problems due to the memory effect in fractional derivatives. In this work, the 2D fractional subdiffusion problems are solved by an algorithm that couples an adaptive time stepping and adaptive spatial basis selection approach. The proposed algorithm is also used to simulate a subdiffusion-convection equation.

AB - The growing number of applications of fractional derivatives in various fields of science and engineering indicates that there is a significant demand for better mathematical algorithms for models with real objects and processes. Currently, most algorithms are designed for 1D problems due to the memory effect in fractional derivatives. In this work, the 2D fractional subdiffusion problems are solved by an algorithm that couples an adaptive time stepping and adaptive spatial basis selection approach. The proposed algorithm is also used to simulate a subdiffusion-convection equation.

KW - Fractional differential equations

KW - Kansa’s method

KW - Radial basis functions

KW - Collocation

KW - Adaptive greedy algorithm

KW - Geometric time grids

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M3 - Journal article

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VL - 229

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EP - 6622

JO - Journal of Computational Physics

JF - Journal of Computational Physics

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ER -

Numerical simulations of 2D fractional subdiffusion problems

Abstract

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