Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

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

Language

English

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. © 2012 Elsevier Ltd. All rights reserved.

Keywords

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

Publication Date

2012

Source Publication Title

Engineering Analysis with Boundary Elements

Volume

36

Issue

11

Start Page

1522

End Page

1527

Publisher

Elsevier

DOI

10.1016/j.enganabound.2012.05.005

ISSN (print)

09557997

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