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

被引：65
|
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
  • [1] Using Non-Standard Finite Difference Scheme to Study Classical and Fractional Order SEIVR Model
    Din, Rahim Ud
    Khan, Khalid Ali
    Aloqaily, Ahmad
    Mlaiki, Nabil
    Alrabaiah, Hussam
    FRACTAL AND FRACTIONAL, 2023, 7 (07)
  • [2] A non-standard finite-difference scheme for conservative oscillators
    Mickens, RE
    JOURNAL OF SOUND AND VIBRATION, 2001, 240 (03) : 587 - 591
  • [3] A non-standard finite difference scheme for convection in a porous cavity
    Moaddy, K.
    Hashim, I.
    Saleh, H.
    JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2012, 18 (03) : 461 - 469
  • [4] A non-standard finite difference scheme for an epidemic model with vaccination
    Ding, Deqiong
    Ma, Qiang
    Ding, Xiaohua
    JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2013, 19 (02) : 179 - 190
  • [5] A non-standard finite difference scheme for the equations modelling stellar structure
    Mickens, RE
    JOURNAL OF SOUND AND VIBRATION, 2003, 265 (05) : 1116 - 1120
  • [6] Stability and numerical analysis via non-standard finite difference scheme of a nonlinear classical and fractional order model
    Alrabaiah, Hussam
    Din, Rahim Ud
    Ansari, Khursheed J.
    Irshad, Ateeq ur Rehman
    Ozdemir, Burhanettin
    RESULTS IN PHYSICS, 2023, 49
  • [7] An Efficient Non-standard Finite Difference Scheme for Solving Distributed Order Time Fractional Reaction–Diffusion Equation
    Taghipour M.
    Aminikhah H.
    International Journal of Applied and Computational Mathematics, 2022, 8 (2)
  • [8] Design and stability analysis of an implicit non-standard finite difference scheme for fractional neutron point kinetic equation
    Roul, Pradip
    Goura, V. M. K. Prasad
    Madduri, Harshita
    Obaidurrahman, K.
    APPLIED NUMERICAL MATHEMATICS, 2019, 145 : 201 - 226
  • [9] DEVELOPMENT OF A NON-STANDARD FINITE DIFFERENCE METHOD FOR SOLVING A FRACTIONAL DECAY MODEL
    Al Kathiri, Said
    Bashier, Eihab
    Abd Hamid, Nur Nadiah
    Ramli, Norshafira
    JOURNAL OF APPLIED MATHEMATICS & INFORMATICS, 2024, 42 (03): : 695 - 708
  • [10] A non-standard finite difference scheme for an advection-diffusion-reaction equation
    Qin, Wendi
    Ding, Deqiong
    Ding, Xiaohua
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2015, 38 (15) : 3308 - 3321
12345