A note on the adaptive numerical solution of a Riemann-Liouville space-fractional Kawarada problem

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:374

Article

Zhu, Lin¹  Sheng, Qin^2,3 

[1] Ningxia Univ, Sch Math & Stat, Yinchuan 750021, Ningxia, Peoples R China

[2] Baylor Univ, Dept Math, Waco, TX 76798 USA

[3] Baylor Univ, Ctr Astrophys Space Phys & Engn Res, Waco, TX 76798 USA

关键词: Fractional Kawarada problem;    Positivity;    Monotonicity;    Critical length;    Quenching time;    Quenching location;   

DOI  :  10.1016/j.cam.2020.112714

来源: Elsevier

【 摘 要 】

This paper concerns the approximation and numerical solution of a singular fractional reaction-diffusion problem. A Riemann-Liouville space-fractional derivative oriented Laplacian is incorporated. While our spatial discretization is fulfilled though combined standard and shifted Grunwald formulas, temporal integration is accomplished via an implicit adaptive Crank-Nicolson scheme. It is proven that under proper constraints of the spatial and temporal discretization parameters, the numerical procedure implemented is positive, monotone and numerically stable. Simulation experiments are given to validate correlations between the fractional derivative and critical values including critical lengths, quenching times and locations. (C) 2020 Published by Elsevier B.V.

【 授权许可】

Free