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Numerical approximations to a fractional Kawarada quenching problem

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  • Beauregard, Matthew A.

Abstract

A numerical approximation is developed, analyzed, and investigated for quenching solutions to a degenerate Kawarada problem with a left and right Riemann-Liouville fractional Laplacian over a finite one dimensional domain. The numerical analysis provides criterion for the numerical approximations to be monotonic, nonnegative, and linearly stable throughout the computation. The numerical algorithm is used to develop an experimental scaling law relating the critical quenching domain size to the order of fractional derivative. Additional experiments indicate that imbalanced left and right derivative transport coefficients can attenuate or prevent quenching from occurring.

Suggested Citation

  • Beauregard, Matthew A., 2019. "Numerical approximations to a fractional Kawarada quenching problem," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 14-22.
    • Handle: RePEc:eee:apmaco:v:349:y:2019:i:c:p:14-22
    DOI: 10.1016/j.amc.2018.12.029
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    References listed on IDEAS

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    1. Beauregard, Matthew A., 2015. "Numerical solutions to singular reaction–diffusion equation over elliptical domains," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 75-91.
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    Cited by:

    1. 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).

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