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A simulation expressivity of the quenching phenomenon in a two-sided space-fractional diffusion equation

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  • Zhu, Lin
  • Liu, Nabing
  • Sheng, Qin

Abstract

The aims of this paper are to investigate and propose a numerical approximation for a quenching type diffusion problem associated with a two-sided Riemann-Liouville space-fractional derivative. The approach adopts weighted Grünwald formulas for suitable spatial discretization. An implicit Crank-Nicolson scheme combined with adaptive technology is then implemented for a temporal integration. Monotonicity, positivity preservation and linearized stability are proved under suitable constraints on spatial and temporal discretization parameters. Two specially designed simulation experiments are presented for illustrating and outreaching properties of the numerical method constructed. Connections between the two-sided fractional differential operator and critical values including quenching time, critical length and quenching location are investigated.

Suggested Citation

  • Zhu, Lin & Liu, Nabing & Sheng, Qin, 2023. "A simulation expressivity of the quenching phenomenon in a two-sided space-fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 437(C).
    • Handle: RePEc:eee:apmaco:v:437:y:2023:i:c:s0096300322005975
    DOI: 10.1016/j.amc.2022.127523
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    References listed on IDEAS

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    1. Guo, Tian Liang & Zhang, KanJian, 2015. "Impulsive fractional partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 581-590.
    2. Zhou, Jun, 2017. "Quenching for a parabolic equation with variable coefficient modeling MEMS technology," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 7-11.
    3. Martínez, Romeo & Macías-Díaz, Jorge E. & Sheng, Qin, 2022. "A nonlinear discrete model for approximating a conservative multi-fractional Zakharov system: Analysis and computational simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 1-21.
    4. Beauregard, Matthew A., 2019. "Numerical approximations to a fractional Kawarada quenching problem," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 14-22.
    5. Nina Garcia-Montoya & Julienne Kabre & Jorge E. Macías-Díaz & Qin Sheng & Chris Goodrich, 2021. "Second-Order Semi-Discretized Schemes for Solving Stochastic Quenching Models on Arbitrary Spatial Grids," Discrete Dynamics in Nature and Society, Hindawi, vol. 2021, pages 1-19, May.
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