IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v205y2023icp340-367.html
   My bibliography  Save this article

Barycentric interpolation collocation algorithm to solve fractional differential equations

Author

Listed:
  • Li, Jin
  • Su, Xiaoning
  • Zhao, Kaiyan

Abstract

Fractional equations have been paid much attention in recent years. Barycentric interpolation collocation algorithm (BICA) is proposed to solve the fractional differential equations in this manuscript. In order to calculate fractional derivatives in fractional differential equations, the Gauss quadrature formula with weights ρ(τ)=(t−τ)ξ−α is constructed and the error estimation of this quadrature formula is proved. The fractional differential term of equation is transformed into Riemann integral under Caputo definition. Barycentric interpolation is used to approximate the unknown function and matrix equation of transformed fractional differential equation is obtained by BICA. The error results show exponential convergence rate of Gauss quadrature formula with weights ρ(τ)=(t−τ)ξ−α by comparing with the Gauss–Legendre quadrature formula. In addition, several examples are given to solve the fractional differential equation.

Suggested Citation

  • Li, Jin & Su, Xiaoning & Zhao, Kaiyan, 2023. "Barycentric interpolation collocation algorithm to solve fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 340-367.
    • Handle: RePEc:eee:matcom:v:205:y:2023:i:c:p:340-367
    DOI: 10.1016/j.matcom.2022.10.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422004062
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.10.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ping Yu & Hongju Li & Jian Ding & Yanli Ma & Hijaz Ahmad, 2021. "Boundary Value Problems of Nonlinear Mixed-Type Fractional Differential Equations," Journal of Mathematics, Hindawi, vol. 2021, pages 1-8, March.
    2. Peichen Zhao & Yongling Cheng & Ram Jiwari, 2021. "Linear Barycentric Rational Method for Solving Schrodinger Equation," Journal of Mathematics, Hindawi, vol. 2021, pages 1-7, October.
    3. 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).
    4. Wang, Nan & Shi, Dongyang, 2021. "Two efficient spectral methods for the nonlinear fractional wave equation in unbounded domain," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 696-718.
    5. Lifei Wu & Xiaozhong Yang, 2020. "An Efficient Alternating Segment Parallel Difference Method for the Time Fractional Telegraph Equation," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-11, March.
    6. Wubshet Ibrahim & Lelisa Kebena Bijiga, 2021. "Neural Network Method for Solving Time-Fractional Telegraph Equation," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-10, May.
    7. Vargas, Antonio M., 2022. "Finite difference method for solving fractional differential equations at irregular meshes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 204-216.
    8. Qu, Haidong & She, Zihang & Liu, Xuan, 2021. "Neural network method for solving fractional diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fang, Xing & Qiao, Leijie & Zhang, Fengyang & Sun, Fuming, 2023. "Explore deep network for a class of fractional partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    2. Heydari, M.H. & Razzaghi, M. & Rouzegar, J., 2022. "Chebyshev cardinal polynomials for delay distributed-order fractional fourth-order sub-diffusion equation," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Qu, Hai-Dong & Liu, Xuan & Lu, Xin & ur Rahman, Mati & She, Zi-Hang, 2022. "Neural network method for solving nonlinear fractional advection-diffusion equation with spatiotemporal variable-order," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    4. Hajimohammadi, Zeinab & Baharifard, Fatemeh & Ghodsi, Ali & Parand, Kourosh, 2021. "Fractional Chebyshev deep neural network (FCDNN) for solving differential models," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    5. Yang, Changqing, 2023. "Improved spectral deferred correction methods for fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    6. Mohamed Kharrat & Hassen Arfaoui, 2023. "A New Stabled Relaxation Method for Pricing European Options Under the Time-Fractional Vasicek Model," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1745-1763, April.
    7. Zhu, Zhen & Lu, Jun-Guo, 2021. "Robust stability and stabilization of hybrid fractional-order multi-dimensional systems with interval uncertainties: An LMI approach," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    8. Li, Hang & Shen, Yongjun & Han, Yanjun & Dong, Jinlu & Li, Jian, 2023. "Determining Lyapunov exponents of fractional-order systems: A general method based on memory principle," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    9. Cui, Yuhuan & Qu, Jingguo & Han, Cundi & Cheng, Gang & Zhang, Wei & Chen, Yiming, 2022. "Shifted Bernstein–Legendre polynomial collocation algorithm for numerical analysis of viscoelastic Euler–Bernoulli beam with variable order fractional model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 361-376.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:205:y:2023:i:c:p:340-367. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.