Department of Mathematics
Meshless simulations of the two-dimensional fractional-time convection–diffusion–reaction equations
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.
Fractional differential equations, Geometric time grids, Memory effect, Meshless local Petrov-Galerkin, Moving least-squares
Source Publication Title
Engineering Analysis with Boundary Elements
Link to Publisher's Edition
Shirzadi, Ahmad, Leevan Ling, and Saeid Abbasbandy. "Meshless simulations of the two-dimensional fractional-time convection–diffusion–reaction equations." Engineering Analysis with Boundary Elements 36.11 (2012): 1522-1527.