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 › Article › peer-review

98 Citations (Scopus)

4 Downloads (Pure)

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
DOIs	https://doi.org/10.1016/j.jcp.2010.05.015
Publication status	Published - Sep 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

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

Access to Document

10.1016/j.jcp.2010.05.015

Full Text

Cite this

@article{f27ea8616f4642fe8a06abcecdbe4a38,

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 = "Adaptive greedy algorithm, Collocation, Fractional differential equations, Geometric time grids, Kansa's method, Radial basis functions",

author = "Hermann BRUNNER and Leevan LING and Masahiro Yamamoto",

year = "2010",

month = sep,

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

language = "English",

volume = "229",

pages = "6613--6622",

journal = "Journal of Computational Physics",

issn = "0021-9991",

publisher = "Academic Press Inc.",

number = "18",

}

TY - JOUR

T1 - Numerical simulations of 2D fractional subdiffusion problems

AU - BRUNNER, Hermann

AU - LING, Leevan

AU - Yamamoto, Masahiro

PY - 2010/9

Y1 - 2010/9

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 - Adaptive greedy algorithm

KW - Collocation

KW - Fractional differential equations

KW - Geometric time grids

KW - Kansa's method

KW - Radial basis functions

UR - http://www.scopus.com/inward/record.url?scp=77954142858&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2010.05.015

DO - 10.1016/j.jcp.2010.05.015

M3 - Article

AN - SCOPUS:77954142858

VL - 229

SP - 6613

EP - 6622

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 18

ER -

Numerical simulations of 2D fractional subdiffusion problems

Abstract

Scopus Subject Areas

User-Defined Keywords

Access to Document

Other files and links

Fingerprint

Cite this