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Numerical analysis for Navier–Stokes equations with time fractional derivatives

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  • Zhang, Jun
  • Wang, JinRong

Abstract

In this article, we study numerical approximation for a class of Navier–Stokes equations with time fractional derivatives. We propose a scheme using finite difference approach in fractional derivative and Legendre-spectral method approximations in space and prove that the scheme is unconditionally stable. In addition, the error estimate shows that the numerical solutions converge with the order O(Δt2−α+Δt−αN1−s), 0 < α < 1 being the order of the fractional derivative in time. Numerical examples are illustrated to verify the theoretical results.

Suggested Citation

  • Zhang, Jun & Wang, JinRong, 2018. "Numerical analysis for Navier–Stokes equations with time fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 481-489.
    • Handle: RePEc:eee:apmaco:v:336:y:2018:i:c:p:481-489
    DOI: 10.1016/j.amc.2018.04.036
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    References listed on IDEAS

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    1. Li, Mengmeng & Wang, JinRong, 2018. "Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 254-265.
    2. Lu, Zuliang & Zhang, Shuhua, 2017. "L∞-error estimates of rectangular mixed finite element methods for bilinear optimal control problem," Applied Mathematics and Computation, Elsevier, vol. 300(C), pages 79-94.
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    Cited by:

    1. Kui Liu & Michal Fečkan & D. O’Regan & JinRong Wang, 2019. "Hyers–Ulam Stability and Existence of Solutions for Differential Equations with Caputo–Fabrizio Fractional Derivative," Mathematics, MDPI, vol. 7(4), pages 1-14, April.
    2. Wang, Mei & Du, Feifei & Chen, Churong & Jia, Baoguo, 2019. "Asymptotic stability of (q, h)-fractional difference equations," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 158-167.
    3. Yu Chen & JinRong Wang, 2019. "Continuous Dependence of Solutions of Integer and Fractional Order Non-Instantaneous Impulsive Equations with Random Impulsive and Junction Points," Mathematics, MDPI, vol. 7(4), pages 1-13, April.
    4. Jang, Bongsoo & Kim, Hyunju, 2024. "Mapping techniques for collocation method of time-fractional convection–diffusion equations in domains with cracks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 60-79.
    5. Xu, Changjin & Liao, Maoxin & Li, Peiluan & Guo, Ying & Xiao, Qimei & Yuan, Shuai, 2019. "Influence of multiple time delays on bifurcation of fractional-order neural networks," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 565-582.

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