Numerical Algorithm to Solve a Class of Variable Order Fractional Integral-Differential Equation Based on Chebyshev Polynomials

被引：15
|
作者：
Sun, Kangwen [1 ]
Zhu, Ming [1 ]
机构：
[1] Beihang Univ, Sch Aeronaut Sci & Technol, Beijing 100191, Peoples R China
来源：
MATHEMATICAL PROBLEMS IN ENGINEERING | 2015年 / 2015卷
基金：
中国国家自然科学基金;
关键词：
TRANSFORM METHOD; APPROXIMATION;
D O I：
10.1155/2015/902161
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
The purpose of this paper is to study the Chebyshev polynomials for the solution of a class of variable order fractional integral-differential equation. The properties of Chebyshev polynomials together with the four kinds of operational matrixes of Chebyshev polynomials are used to reduce the problem to the solution of a system of algebraic equations. By solving the algebraic equations, the numerical solutions are acquired. Further some numerical examples are shown to illustrate the accuracy and reliability of the proposed approach and the results have been compared with the exact solution.
引用
收藏
页数：10
相关论文
共 50 条
  • [21] Numerical approach for a class of distributed order time fractional partial differential equations
    Moghaddam, B. P.
    Tenreiro Machado, J. A.
    Morgado, M. L.
    APPLIED NUMERICAL MATHEMATICS, 2019, 136 : 152 - 162
  • [22] Numerical Algorithm to Solve Fractional Integro-differential Equations Based on Operational Matrix of Generalized Block Pulse Functions
    Ma, Yunpeng
    Wang, Lifeng
    Meng, Zhijun
    CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 2013, 96 (01): : 31 - 47
  • [23] A high order numerical method for the variable order time-fractional reaction-subdiffusion equation
    Rajput, Priyanka
    Srivastava, Nikhil
    Singh, Vineet Kumar
    CHINESE JOURNAL OF PHYSICS, 2023, 85 : 431 - 444
  • [24] Chebyshev cardinal wavelets for nonlinear stochastic differential equations driven with variable-order fractional Brownian motion
    Heydari, M. H.
    Avazzadeh, Z.
    Mahmoudi, M. R.
    CHAOS SOLITONS & FRACTALS, 2019, 124 : 105 - 124
  • [25] A NUMERICAL ALGORITHM FOR A CLASS OF NONLINEAR FRACTIONAL VOLTERRA INTEGRAL EQUATIONS VIA MODIFIED HAT FUNCTIONS
    Biazar, Jafar
    Ebrahimi, Hamed
    JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS, 2022, 34 (03) : 295 - 316
  • [26] Numerical simulation for two-dimensional variable-order fractional nonlinear cable equation
    Bhrawy, A. H.
    Zaky, M. A.
    NONLINEAR DYNAMICS, 2015, 80 (1-2) : 101 - 116
  • [27] A Tau Approach for Solving Time-Fractional Heat Equation Based on the Shifted Sixth-Kind Chebyshev Polynomials
    Abdelghany, Esraa Magdy
    Abd-Elhameed, Waleed Mohamed
    Moatimid, Galal Mahrous
    Youssri, Youssri Hassan
    Atta, Ahmed Gamal
    SYMMETRY-BASEL, 2023, 15 (03):
  • [28] 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
  • [29] Numerical solution of nonlinear stochastic integral equation by stochastic operational matrix based on Bernstein polynomials
    Asgari, Mahnaz
    Hashemizadeh, Elham
    Khodabin, Morteza
    Maleknejad, Khosrow
    BULLETIN MATHEMATIQUE DE LA SOCIETE DES SCIENCES MATHEMATIQUES DE ROUMANIE, 2014, 57 (01): : 3 - 12
  • [30] NUMERICAL METHODS FOR THE VARIABLE-ORDER FRACTIONAL ADVECTION-DIFFUSION EQUATION WITH A NONLINEAR SOURCE TERM
    Zhuang, P.
    Liu, F.
    Anh, V.
    Turner, I.
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2009, 47 (03) : 1760 - 1781
12345