Nonstandard finite difference method for solving complex-order fractional Burgers' equations

被引：15
|
作者：
Sweilam, N. H. [1 ]
AL-Mekhlafi, S. M. [2 ]
Baleanu, D. [3 ,4 ]
机构：
[1] Cairo Univ, Dept Math, Fac Sci, Giza, Egypt
[2] Sanaa Univ, Fac Educ, Dept Math, Sanaa, Yemen
[3] Cankaya Univ, Dept Math, Etimesgut, Turkey
[4] Inst Space Sci, Magurele, Romania
来源：
JOURNAL OF ADVANCED RESEARCH | 2020年 / 25卷
关键词：
Burgers' equations; Complex order fractional derivative; Nonstandard weighted average finite difference method; Stability analysis; NONLINEAR PDES; DERIVATIVES; CALCULUS; MODEL;
D O I：
10.1016/j.jare.2020.04.007
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
The aim of this work is to present numerical treatments to a complex order fractional nonlinear one-dimensional problem of Burgers' equations. A new parameter sigma(t) is presented in order to be consistent with the physical model problem. This parameter characterizes the existence of fractional structures in the equations. A relation between the parameter sigma(t) and the time derivative complex order is derived. An unconditionally stable numerical scheme using a kind of weighted average nonstandard finite-difference discretization is presented. Stability analysis of this method is studied. Numerical simulations are given to confirm the reliability of the proposed method. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Cairo University.
引用
收藏
页码：19 / 29
页数：11
相关论文
共 50 条
  • [31] Solving the Advection Diffusion Reaction Equations by Using the Enhanced Higher-Order Unconditionally Positive Finite Difference Method
    Ndou, Ndivhuwo
    Dlamini, Phumlani
    Jacobs, Byron Alexander
    MATHEMATICS, 2024, 12 (07)
  • [32] The Order of Convergence of Difference Schemes for Fractional Equations
    Liu, Ru
    Li, Miao
    Piskarev, Sergey
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2017, 38 (06) : 754 - 769
  • [33] Modification of the Optimal Auxiliary Function Method for Solving Fractional Order KdV Equations
    Ullah, Hakeem
    Fiza, Mehreen
    Khan, Ilyas
    Alshammari, Nawa
    Hamadneh, Nawaf N.
    Islam, Saeed
    FRACTAL AND FRACTIONAL, 2022, 6 (06)
  • [34] An efficient algorithm for solving the variable-order time-fractional generalized Burgers' equation
    Rawani, Mukesh Kumar
    Verma, Amit Kumar
    Cattani, Carlo
    JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2024, 70 (06) : 5269 - 5291
  • [35] Finite difference-finite element approach for solving fractional Oldroyd-B equation
    Rasheed, Amer
    Wahab, Abdul
    Shah, Shaista Qaim
    Nawaz, Rab
    ADVANCES IN DIFFERENCE EQUATIONS, 2016,
  • [36] FRACTIONAL CHEBYSHEV COLLOCATION METHOD FOR SOLVING LINEAR FRACTIONAL-ORDER DELAY-DIFFERENTIAL EQUATIONS
    Dabiri, Arman
    Butcher, Eric A.
    PROCEEDINGS OF THE ASME INTERNATIONAL DESIGN ENGINEERING TECHNICAL CONFERENCES AND COMPUTERS AND INFORMATION IN ENGINEERING CONFERENCE, 2017, VOL 6, 2017,
  • [37] A High-Order Finite-Difference Scheme with a Linearization Technique for Solving of Three-Dimensional Burgers Equation
    Campos, M. D.
    Romao, E. C.
    CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 2014, 103 (03): : 139 - 154
  • [38] Implementation of Fractional Constitutive Equations into the Finite Element Method
    Gaul, L.
    Schmidt, A.
    CHALLENGES IN MECHANICS OF TIME-DEPENDENT MATERIALS, VOL 2, 2015, : 101 - 111
  • [39] Solving fractional pantograph delay differential equations via fractional-order Boubaker polynomials
    Rabiei, Kobra
    Ordokhani, Yadollah
    ENGINEERING WITH COMPUTERS, 2019, 35 (04) : 1431 - 1441
  • [40] The discrete homotopy perturbation method for solving burgers' and heat equations
    Zhu, Hongqing
    Ding, Meiyu
    Journal of Information and Computational Science, 2014, 11 (05): : 1647 - 1657
12345