Method of approximate particular solutions for constant- and variable-order fractional diffusion models

Zhuo Jia Fu*, Wen Chen, Leevan LING

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

86 Citations (Scopus)

Abstract

The method of approximate particular solutions (MAPS) is an alternative radial basis function (RBF) meshless method, which is defined in terms of a linear combination of the particular solutions of the inhomogeneous governing equations with traditional RBFs as the source term. In this paper, we apply the MAPS to both constant- and variable-order time fractional diffusion models. In the discretization formulation, a finite difference scheme and the MAPS are used respectively to discretize time fractional derivative and spatial derivative terms. Numerical investigation examples show the present meshless scheme has highly accuracy and computationally efficiency for various fractional diffusion models.

Original languageEnglish
Pages (from-to)37-46
Number of pages10
JournalEngineering Analysis with Boundary Elements
Volume57
DOIs
Publication statusPublished - 3 Jun 2015

Scopus Subject Areas

  • Analysis
  • Engineering(all)
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Collocation method
  • Fractional diffusion
  • Meshless method
  • Radial basis function

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