Numerical solution of fractional advection-diffusion equation with a nonlinear source term

被引：62
|
作者：
Parvizi, M. [1 ]
Eslahchi, M. R. [1 ]
Dehghan, Mehdi [2 ]
机构：
[1] Tarbiat Modares Univ, Fac Math Sci, Dept Appl Math, Tehran, Iran
[2] Amirkabir Univ Technol, Dept Appl Math, Fac Math & Comp Sci, Tehran 15914, Iran
来源：
NUMERICAL ALGORITHMS | 2015年 / 68卷 / 03期
关键词：
Fractional advection-diffusion equation; Riemann-Liouville derivative; Jacobi polynomials; Operational matrix; Collocation method; Stability analysis and convergence; FINITE-DIFFERENCE APPROXIMATIONS; FUNDAMENTAL SOLUTION; ORDER;
D O I：
10.1007/s11075-014-9863-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we use the Jacobi collocation method for solving a special kind of the fractional advection-diffusion equation with a nonlinear source term. This equation is the classical advection-diffusion equation in which the space derivatives are replaced by the Riemann-Liouville derivatives of order 0 < sigma a parts per thousand currency sign 1 and 1 < mu a parts per thousand currency sign 2. Also the stability and convergence of the presented method are shown for this equation. Finally some numerical examples are solved using the presented method.
引用
收藏
页码：601 / 629
页数：29
相关论文
共 50 条
  • [41] An accurate numerical technique for solving fractional advection-diffusion equation with generalized Caputo derivative
    Nagy, A. M.
    Issa, K.
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2024, 75 (05):
  • [42] A numerical method for a time-fractional advection-dispersion equation with a nonlinear source term
    Mejia, Carlos E.
    Piedrahita, Alejandro
    JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2019, 61 (1-2) : 593 - 609
  • [43] A fast difference scheme for the multi-term time fractional advection-diffusion equation with a non-linear source term
    Dwivedi, Himanshu Kumar
    Rajeev
    CHINESE JOURNAL OF PHYSICS, 2024, 89 : 86 - 103
  • [44] PARAMETER ESTIMATION IN NONLINEAR COUPLED ADVECTION-DIFFUSION EQUATION
    Ferdinand, Robert R.
    APPLICATIONS AND APPLIED MATHEMATICS-AN INTERNATIONAL JOURNAL, 2007, 2 (01): : 1 - 13
  • [45] On stable and explicit numerical methods for the advection-diffusion equation
    Witek, Marcin L.
    Teixeira, Joao
    Flatau, Piotr J.
    MATHEMATICS AND COMPUTERS IN SIMULATION, 2008, 79 (03) : 561 - 570
  • [46] NUMERICAL SOLUTION OF FRACTIONAL ORDER ADVECTION-REACTION-DIFFUSION EQUATION
    Das, Subir
    Singh, Anup
    Ong, Seng Huat
    THERMAL SCIENCE, 2018, 22 : S309 - S316
  • [47] A solution of the time-dependent advection-diffusion equation
    Tirabassi, Tiziano
    Silva, Everson J. G.
    Buske, Daniela
    Vilhena, Marco T.
    INTERNATIONAL JOURNAL OF ENVIRONMENT AND POLLUTION, 2019, 65 (1-3) : 211 - 228
  • [48] AN APPROXIMATE SOLUTION TO THE ADVECTION-DIFFUSION EQUATION AS APPLIED TO AN ESTUARY
    WANG, ST
    MCMILLAN, AF
    CHEN, BH
    JOURNAL OF HYDROLOGY, 1980, 48 (3-4) : 251 - 268
  • [49] NONLINEAR INSTABILITY IN ADVECTION-DIFFUSION NUMERICAL MODELS.
    Adam, Y.
    1600, (09):
  • [50] Estimate of the fractional advection-diffusion equation with a time-fractional term based on the shifted Legendre polynomials
    Aghdam, Yones Esmaeelzade
    Mesgarani, Hamid
    Asadi, Zeynab
    JOURNAL OF MATHEMATICAL MODELING, 2023, 11 (04): : 731 - 744
12345