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

Lin Zhu, Rumin Dong and Qin Sheng

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 244, issue C, 196-212

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.

Keywords: Riemann–Liouville fractional-order derivatives; Positivity; Monotonicity; Stability; Quenching time; Convergence (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:244:y:2026:i:c:p:196-212

DOI: 10.1016/j.matcom.2025.12.019

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