Numerical Solution of the Time-Fractional Sub-Diffusion Equation on an Unbounded Domain in Two-Dimensional Space

Hongwei Li, Xiaonan WU, Jiwei Zhang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

Abstract

The numerical solution of the time-fractional sub-diffusion equation on an unbounded domain in two-dimensional space is considered, where a circular artificial boundary is introduced to divide the unbounded domain into a bounded computational domain and an unbounded exterior domain. The local artificial boundary conditions for the fractional sub-diffusion equation are designed on the circular artificial boundary by a joint Laplace transform and Fourier series expansion, and some auxiliary variables are introduced to circumvent high-order derivatives in the artificial boundary conditions. The original problem defined on the unbounded domain is thus reduced to an initial boundary value problem on a bounded computational domain. A finite difference and L1 approximation are applied for the space variables and the Caputo time-fractional derivative, respectively. Two numerical examples demonstrate the performance of the proposed method.

Original languageEnglish
Pages (from-to)439-454
Number of pages16
JournalEast Asian Journal on Applied Mathematics
Volume7
Issue number3
DOIs
Publication statusPublished - 1 Aug 2017

Scopus Subject Areas

  • Applied Mathematics

User-Defined Keywords

  • Caputo time-fractional derivative
  • finite difference method
  • Fractional sub-diffusion equation
  • local artificial boundary conditions
  • unbounded domain

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