Journal
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
Volume 36, Issue 11, Pages 1522-1527Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.enganabound.2012.05.005
Keywords
Fractional differential equations; Meshless local Petrov-Galerkin; Moving least-squares; Geometric time grids; Memory effect
Funding
- CERG Grant of the Hong Kong Research Grant Council
- FRG Grant of the Hong Kong Baptist University
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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. (C) 2012 Elsevier Ltd. All rights reserved.
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