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A semi-adaptive discrete variable method for emulating dual space fractional convection–diffusion quenching problems

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  • Zhu, Lin
  • Dong, Rumin
  • Sheng, Qin

Abstract

This paper investigates the properties of discrete variable approximations for the quenching solutions of a nonlinear one-dimensional dual Riemann–Liouville fractional-order problem. The fractional-order spatial derivatives are discretized using a weighted average approach, combined with both the standard and shifted Grünwald formulas. The advection term is approximated via a direct Euler scheme, resulting in a semi-discretized system of nonlinear, constant-coefficient equations. The robustness of the proposed discrete variable method is demonstrated and validated through rigorous mathematical analysis and numerical experiments. The study systematically examines the effects of the critical length, convective terms, and the two fractional orders on the quenching phenomenon. Detailed computational results and analyses provide a deeper understanding of quenching behavior in nonlinear fractional-order problems.

Suggested Citation

  • Zhu, Lin & Dong, Rumin & Sheng, Qin, 2026. "A semi-adaptive discrete variable method for emulating dual space fractional convection–diffusion quenching problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 244(C), pages 196-212.
    • Handle: RePEc:eee:matcom:v:244:y:2026:i:c:p:196-212
    DOI: 10.1016/j.matcom.2025.12.019
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    References listed on IDEAS

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    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).
    2. Dongdong Gao & Jianli Li, 2021. "New results for impulsive fractional differential equations through variational methods," Mathematische Nachrichten, Wiley Blackwell, vol. 294(10), pages 1866-1878, October.
    3. Beauregard, Matthew A., 2019. "Numerical approximations to a fractional Kawarada quenching problem," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 14-22.
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