user

NUMERICAL METHODS FOR THE VARIABLE-ORDER FRACTIONAL ADVECTION-DIFFUSION EQUATION WITH A NONLINEAR SOURCE TERM

被引：450
|
作者：
Zhuang, P. [1 ]
Liu, F. [2 ,3 ]
Anh, V. [2 ]
Turner, I. [2 ]
机构：
[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
[2] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia
[3] S China Univ Technol, Sch Math Sci, Guangzhou 510640, Guangdong, Peoples R China
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2009年 / 47卷 / 03期
基金：
澳大利亚研究理事会; 中国国家自然科学基金;
关键词：
fractional derivative of variable order; nonlinear fractional advection-diffusion equation; finite difference methods; method of lines; extrapolation method; stability and convergence; DISPERSION EQUATIONS; FELLER SEMIGROUPS; APPROXIMATION; DIFFERENTIATION; OPERATORS;
D O I：
10.1137/080730597
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moveover, we also present a fractional method of lines, a matrix transfer technique, and an extrapolation method for the equation. Some numerical examples are given, and the results demonstrate the effectiveness of theoretical analysis.
引用
收藏
页码：1760 / 1781
页数：22
相关论文
共 50 条
  • [21] Numerical Method for Fractional Advection-Diffusion Equation with Heredity
    Pimenov V.G.
    [J]. Journal of Mathematical Sciences, 2018, 230 (5) : 737 - 741
  • [22] A second-order numerical method for nonlinear variable-order fractional diffusion equation with time delay
    Li, Jing
    Kang, Xinyue
    Shi, Xingyun
    Song, Yufei
    [J]. MATHEMATICS AND COMPUTERS IN SIMULATION, 2024, 219 : 101 - 111
  • [23] Analysis and numerical solution of a nonlinear variable-order fractional differential equation
    Hong Wang
    Xiangcheng Zheng
    [J]. Advances in Computational Mathematics, 2019, 45 : 2647 - 2675
  • [24] Analysis and numerical solution of a nonlinear variable-order fractional differential equation
    Wang, Hong
    Zheng, Xiangcheng
    [J]. ADVANCES IN COMPUTATIONAL MATHEMATICS, 2019, 45 (5-6) : 2647 - 2675
  • [25] A stable RBF-FD method for solving two-dimensional variable-order time fractional advection-diffusion equation
    Biglari, Marzieh
    Soheili, Ali R.
    Toutounian, Faezeh
    [J]. ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2023, 152 : 582 - 597
  • [26] Numerical simulation of fractional advection-diffusion equation: A method to anomalous diffusion
    Xia, Y.
    Wu, J. C.
    [J]. CALIBRATION AND RELIABILITY IN GROUNDWATER MODELING: MANAGING GROUNDWATER AND THE ENVIRONMENT, 2009, : 433 - 436
  • [27] On stable and explicit numerical methods for the advection-diffusion equation
    Witek, Marcin L.
    Teixeira, Joao
    Flatau, Piotr J.
    [J]. MATHEMATICS AND COMPUTERS IN SIMULATION, 2008, 79 (03) : 561 - 570
  • [28] Numerical Solution of Advection-Diffusion Equation of Fractional Order Using Chebyshev Collocation Method
    Ali Shah, Farman
    Boulila, Wadii
    Koubaa, Anis
    Mlaiki, Nabil
    [J]. FRACTAL AND FRACTIONAL, 2023, 7 (10)
  • [29] A Numerical Algorithm for the Caputo Tempered Fractional Advection-Diffusion Equation
    Wenhui Guan
    Xuenian Cao
    [J]. Communications on Applied Mathematics and Computation, 2021, 3 : 41 - 59
  • [30] Analytical and Numerical Solutions of Fractional Type Advection-diffusion Equation
    Jannelli, Alessandra
    Ruggieri, Marianna
    Speciale, Maria Paola
    [J]. PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2016 (ICNAAM-2016), 2017, 1863
12345