期刊
APPLIED MATHEMATICAL MODELLING
卷 78, 期 -, 页码 539-549出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2019.09.055
关键词
Generalized finite difference (GFD) approach; Time fractional diffusion equation; Variable-order derivatives; Meshless methods; Three-dimensional arbitrary domains
资金
- National Natural Science Foundation of China [11872220, 71571108, 11572112]
- Natural Science Foundation of Shandong Province of China [ZR2017JL004]
In this study a new framework for solving three-dimensional (3D) time fractional diffusion equation with variable-order derivatives is presented. Firstly, a theta-weighted finite difference scheme with second-order accuracy is introduced to perform temporal discretization. Then a meshless generalized finite difference (GFD) scheme is employed for the solutions of remaining problems in the space domain. The proposed scheme is truly meshless and can be used to solve problems defined on an arbitrary domain in three dimensions. Preliminary numerical examples illustrate that the new method proposed here is accurate and efficient for time fractional diffusion equation in three dimensions, particularly when high accuracy is desired. (C) 2019 Elsevier Inc. All rights reserved.
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