The non-standard finite difference scheme for linear fractional PDEs in fluid mechanics

被引：68
|
作者：
Moaddy, K. [2 ]
Momani, S. [1 ]
Hashim, I. [2 ]
机构：
[1] Univ Jordan, Fac Sci, Dept Math, Amman 11942, Jordan
[2] Univ Kebangsaan Malaysia, Sch Math Sci, Ukm Bangi Selangor 43600, Malaysia
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2011年 / 61卷 / 04期
关键词：
Non-standard finite difference schemes; Fractional differential equations; Telegraph equation; Wave equation; Burgers equation; EQUATIONS; CHAOS;
D O I：
10.1016/j.camwa.2010.12.072
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A non-standard finite difference scheme is developed to solve the linear partial differential equations with time- and space-fractional derivatives. The Grunwald-Letnikov method is used to approximate the fractional derivatives. Numerical illustrations that include the linear inhomogeneous time-fractional equation, linear space-fractional telegraph equation, linear inhomogeneous fractional Burgers equation and the fractional wave equation are investigated to show the pertinent features of the technique. Numerical results are presented graphically and reveal that the non-standard finite difference scheme is very effective and convenient for solving linear partial differential equations of fractional order. (C) 2010 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1209 / 1216
页数：8
相关论文
共 50 条
  • [41] Non-standard finite difference schemes for multi-dimensional second-order systems in non-smooth mechanics
    Dumont, Yves
    Lubuma, Jean M. -S.
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2007, 30 (07) : 789 - 825
  • [42] On non-standard finite difference models of reaction-diffusion equations
    Anguelov, R
    Kama, P
    Lubuma, JMS
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 175 (01) : 11 - 29
  • [43] A comparative epidemiological stability analysis of predictor corrector type non-standard finite difference scheme for the transmissibility of measles
    Farooqi, Asma
    Ahmad, Riaz
    Alotaibi, Hammad
    Nofal, Taher A.
    Farooqi, Rashada
    Khan, Ilyas
    RESULTS IN PHYSICS, 2021, 21
  • [44] A convergence-preserving non-standard finite difference scheme for the solutions of singular Lane-Emden equations
    Sunday, Joshua
    Shokri, Ali
    Akinola, Richard Olatokunbo
    Joshua, Kyaharnan Victor
    Nonlaopon, Kamsing
    RESULTS IN PHYSICS, 2022, 42
  • [45] A non-standard finite difference scheme for a delayed and diffusive viral infection model with general nonlinear incidence rate
    Xu, Jinhu
    Geng, Yan
    Hou, Jiangyong
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 74 (08) : 1782 - 1798
  • [46] A non-standard format for continuum mechanics
    Di Carlo, A
    CONTEMPORARY RESEARCH IN THE MECHANICS AND MATHEMATICS OF MATERIALS, 1996, : 92 - 104
  • [47] A linear finite difference scheme for generalized time fractional Burgers equation
    Li, Dongfang
    Zhang, Chengjian
    Ran, Maohua
    APPLIED MATHEMATICAL MODELLING, 2016, 40 (11-12) : 6069 - 6081
  • [48] Non standard finite difference scheme preserving dynamical properties
    Cresson, Jacky
    Pierret, Frederic
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2016, 303 : 15 - 30
  • [49] A Non-Standard Finite Difference Scheme for a Diffusive HIV-1 Infection Model with Immune Response and Intracellular Delay
    Liu, Xiao-Lan
    Zhu, Cheng-Cheng
    AXIOMS, 2022, 11 (03)
  • [50] Stability preserving non-standard finite difference scheme for a harvesting Leslie-Gower predator-prey model
    Darti, Isnani
    Suryanto, Agus
    JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2015, 21 (06) : 528 - 534
12345