A meshless method for solving three-dimensional time fractional diffusion equation with variable-order derivatives

Gu Yan; Sun HongGuang

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A meshless method for solving three-dimensional time fractional diffusion equation with variable-order derivatives

机译：求解含变阶导数的三维时间分数扩散方程的无网格方法

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摘要

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.

机译：在这项研究中，提出了一种求解具有可变阶导数的三维（3D）时间分数扩散方程的新框架。首先，引入具有二阶精度的θ加权有限差分方案来进行时间离散化。然后采用无网格广义有限差分（GFD）方案求解空间域中的剩余问题。所提出的方案是真正无网格的，并且可以用于解决在三维上在任意域上定义的问题。初步的数值算例表明，本文提出的新方法对于三维时间分数扩散方程是准确而高效的，特别是在需要高精度时。（C）2019 Elsevier Inc.保留所有权利。

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来源
《Applied Mathematical Modelling》 |2020年第2期|539-549|共11页
作者
Gu Yan; Sun HongGuang;
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作者单位

Qingdao Univ Sch Math & Stat Qingdao 266071 Shandong Peoples R China;

Hohai Univ Coll Mech & Mat Nanjing 210098 Jiangsu Peoples R China;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Generalized finite difference (GFD) approach; Time fractional diffusion equation; Variable-order derivatives; Meshless methods; Three-dimensional arbitrary domains;

机译：广义有限差分法（GFD）;时间分数扩散方程;可变阶导数;无网格方法;三维任意域;

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2. A meshless method for solving two-dimensional variable-order time fractional advection-diffusion equation [J] . Tayebi A., Shekari Y., Heydari M. H. Journal of Computational Physics . 2017,第期

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3. A fast method for variable-order Caputo fractional derivative with applications to time-fractional diffusion equations [J] . Fang Zhi-Wei, Sun Hai-Wei, Wang Hong Computers & mathematics with applications . 2020,第5期

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5. Meshless Methods for Numerically Solving Boundary Value Problems of Elliptic Type Partial Differential Equations [D] . Choi, Minhwa 2018

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7. The Maximum Principle for Variable-Order Fractional Diffusion Equations and the Estimates of Higher Variable-Order Fractional Derivatives [O] . Guangming Xue, Funing Lin, Guangwang Su 2020

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A meshless method for solving three-dimensional time fractional diffusion equation with variable-order derivatives

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