Department of Mathematics
Method of approximate particular solutions for constant- and variable-order fractional diffusion models
© 2014 Elsevier Ltd. All rights reserved. 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.
Collocation method, Fractional diffusion, Meshless method, Radial basis function
Source Publication Title
Engineering Analysis with Boundary Elements
Fu, Zhuo-Jia, Wen Chen, and Leevan Ling. "Method of approximate particular solutions for constant- and variable-order fractional diffusion models." Engineering Analysis with Boundary Elements 57 (2015): 37-46.