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Finite difference Laguerre-Legendre spectral method for the two-dimensional generalized Oldroyd-B fluid on a semi-infinite domain

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  • Chi, Xiaoqing
  • Jiang, Xiaoyun

Abstract

In this paper, we study the numerical solution for a two-dimensional generalized Oldroyd-B fluid flowing on a semi-infinite domain. The second order θ scheme with the weighted and shifted Grünwald difference operator is derived to approximate the time derivatives with orders in (0,2). For the case of unbounded space, the Laguerre-Legendre spectral method is proposed. The fully discrete scheme is obtained and proved to be stable, convergent with accuracy O(τ2+N(1−s)/2+M1−r), where τ is the time step size, N,M are the polynomial degrees. We also implement some numerical examples to further support the theoretical analysis.

Suggested Citation

  • Chi, Xiaoqing & Jiang, Xiaoyun, 2021. "Finite difference Laguerre-Legendre spectral method for the two-dimensional generalized Oldroyd-B fluid on a semi-infinite domain," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    • Handle: RePEc:eee:apmaco:v:402:y:2021:i:c:s0096300321001867
    DOI: 10.1016/j.amc.2021.126138
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    References listed on IDEAS

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    1. Haidong Qu & Xuan Liu, 2015. "A Numerical Method for Solving Fractional Differential Equations by Using Neural Network," Advances in Mathematical Physics, Hindawi, vol. 2015, pages 1-12, October.
    2. Zhang, Hui & Jiang, Xiaoyun & Yang, Xiu, 2018. "A time-space spectral method for the time-space fractional Fokker–Planck equation and its inverse problem," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 302-318.
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    Cited by:

    1. Liu, Yi & Chi, Xiaoqing & Xu, Huanying & Jiang, Xiaoyun, 2022. "Fast method and convergence analysis for the magnetohydrodynamic flow and heat transfer of fractional Maxwell fluid," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    2. Hossein Hassani & Zakieh Avazzadeh & Praveen Agarwal & Mohammad Javad Ebadi & Ali Bayati Eshkaftaki, 2024. "Generalized Bernoulli–Laguerre Polynomials: Applications in Coupled Nonlinear System of Variable-Order Fractional PDEs," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 371-393, January.

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