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A simulation expressivity of the quenching phenomenon in a two-sided space-fractional diffusion equation
Applied Mathematics and Computation ( IF 4 ) Pub Date : 2022-09-19 , DOI: 10.1016/j.amc.2022.127523
Lin Zhu, Nabing Liu, Qin Sheng

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.



中文翻译:

两侧空间分数扩散方程中淬火现象的模拟表达

本文的目的是研究并提出与两侧 Riemann-Liouville 空间分数导数相关的淬火型扩散问题的数值近似。该方法采用加权 Grünwald 公式进行适当的空间离散化。然后实施与自适应技术相结合的隐式 Crank-Nicolson 方案以进行时间积分。在空间和时间离散化参数的适当约束下证明了单调性、正性保持和线性化稳定性。提出了两个专门设计的模拟实验,以说明和扩展所构建的数值方法的特性。研究了双边分数微分算子与淬火时间、临界长度和淬火位置等临界值之间的联系。

更新日期:2022-09-20
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