Meshless simulations of the two-dimensional fractional-time convection-diffusion-reaction equations

Ahmad Shirzadi*, Leevan LING, Saeid Abbasbandy

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

60 Citations (Scopus)

Abstract

The aim of this work is to propose a numerical approach based on the local weak formulations and finite difference scheme to solve the two-dimensional fractional-time convection-diffusion-reaction equations. The numerical studies on sensitivity analysis to parameter and convergence analysis show that our approach is stable. Moreover, numerical demonstrations are given to show that the weak-form approach is applicable to a wide range of problems; in particular, a forced-subdiffusion-convection equation previously solved by a strong-form approach with weak convection is considered. It is shown that our approach can obtain comparable simulations not only in weak convection but also in convection dominant cases. The simulations to a subdiffusion-convection-reaction equation are also presented.

Original languageEnglish
Pages (from-to)1522-1527
Number of pages6
JournalEngineering Analysis with Boundary Elements
Volume36
Issue number11
DOIs
Publication statusPublished - Nov 2012

Scopus Subject Areas

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

User-Defined Keywords

  • Fractional differential equations
  • Geometric time grids
  • Memory effect
  • Meshless local Petrov-Galerkin
  • Moving least-squares

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