Numerical simulations for space-time fractional diffusion equations

Leevan LING*, Masahiro Yamamoto

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We consider the solutions of a space-time fractional diffusion equation on the interval [-1, 1]. The equation is obtained from the standard diffusion equation by replacing the second-order space derivative by a Riemann-Liouville fractional derivative of order between one and two, and the first-order time derivative by a Caputo fractional derivative of order between zero and one. As the fundamental solution of this fractional equation is unknown (if exists), an eigenfunction approach is applied to obtain approximate fundamental solutions which are then used to solve the space-time fractional diffusion equation with initial and boundary values. Numerical results are presented to demonstrate the effectiveness of the proposed method in long time simulations.

Original languageEnglish
Article number1341001
JournalInternational Journal of Computational Methods
Volume10
Issue number2
DOIs
Publication statusPublished - Mar 2013

Scopus Subject Areas

  • Computer Science (miscellaneous)
  • Computational Mathematics

User-Defined Keywords

  • Approximate fundamental solution
  • Caputo fractional derivative
  • collocation
  • Jacobi-collocation
  • Riemann-Liouville fractional derivative
  • Trefftz method

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