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Numerical algorithm to solve system of nonlinear fractional differential equations based on wavelets method and the error analysis

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  • Chen, Yiming
  • Ke, Xiaohong
  • Wei, Yanqiao

Abstract

In this paper, a system of nonlinear fractional differential equations (FDEs) are considered. They have been solved by Legendre wavelets method combining with its operational matrix. However, there are no articles about solving this system using wavelets method. The main purpose of this technique is to transform the initial equations into a nonlinear system of algebraic equations which can be solved easily. The convergence and error analysis are presented to show the correctness and feasibility of method proposed for solving the above mentioned problem. Finally, the applicability and efficiency of the mentioned approach are demonstrated by three numerical examples.

Suggested Citation

  • Chen, Yiming & Ke, Xiaohong & Wei, Yanqiao, 2015. "Numerical algorithm to solve system of nonlinear fractional differential equations based on wavelets method and the error analysis," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 475-488.
    • Handle: RePEc:eee:apmaco:v:251:y:2015:i:c:p:475-488
    DOI: 10.1016/j.amc.2014.11.079
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    References listed on IDEAS

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    1. Lu, Jun Guo & Chen, Guanrong, 2006. "A note on the fractional-order Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 685-688.
    2. Tavazoei, Mohammad Saleh & Haeri, Mohammad, 2009. "A note on the stability of fractional order systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1566-1576.
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    Cited by:

    1. Pulido, M. Aurora P. & Sousa, J. Vanterler C. & de Oliveira, E. Capelas, 2024. "New discretization of ψ-Caputo fractional derivative and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 135-158.
    2. Rehman, Mujeeb ur & Idrees, Amna & Saeed, Umer, 2017. "A quadrature method for numerical solutions of fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 38-49.
    3. Zhao, Fuqiang & Huang, Qingxue & Xie, Jiaquan & Li, Yugui & Ma, Lifeng & Wang, Jianmei, 2017. "Chebyshev polynomials approach for numerically solving system of two-dimensional fractional PDEs and convergence analysis," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 321-330.
    4. Sun, Lin & Chen, Yiming & Dang, Rongqi & Cheng, Gang & Xie, Jiaquan, 2022. "Shifted Legendre polynomials algorithm used for the numerical analysis of viscoelastic plate with a fractional order model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 190-203.
    5. Sun, Lin & Chen, Yiming, 2021. "Numerical analysis of variable fractional viscoelastic column based on two-dimensional Legendre wavelets algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    6. Doungmo Goufo, Emile F. & Khan, Yasir & Chaudhry, Qasim Ali, 2020. "HIV and shifting epicenters for COVID-19, an alert for some countries," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).

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