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A diffusion–convection problem with a fractional derivative along the trajectory of motion
Russian Journal of Numerical Analysis and Mathematical Modelling ( IF 0.6 ) Pub Date : 2021-06-01 , DOI: 10.1515/rnam-2021-0013 Alexander V. Lapin 1, 2 , Vladimir V. Shaidurov 2, 3
Russian Journal of Numerical Analysis and Mathematical Modelling ( IF 0.6 ) Pub Date : 2021-06-01 , DOI: 10.1515/rnam-2021-0013 Alexander V. Lapin 1, 2 , Vladimir V. Shaidurov 2, 3
Affiliation
A new mathematical model of the diffusion–convective process with ‘memory along the flow path’ is proposed. This process is described by a homogeneous one-dimensional Dirichlet initial-boundary value problem with a fractional derivative along the characteristic curve of the convection operator. A finite-difference approximation of the problem is constructed and investigated. The stability estimates for finite-difference schemes are proved. The accuracy estimates are given for the case of sufficiently smooth input data and the solution.
中文翻译:
沿运动轨迹具有分数阶导数的扩散-对流问题
提出了一种具有“沿流动路径记忆”的扩散-对流过程的新数学模型。这个过程由一个齐次一维狄利克雷初始边界值问题描述,该问题具有沿对流算子特征曲线的分数阶导数。构建并研究了该问题的有限差分近似。证明了有限差分格式的稳定性估计。针对足够平滑的输入数据和解的情况给出了准确度估计。
更新日期:2021-06-24
中文翻译:
沿运动轨迹具有分数阶导数的扩散-对流问题
提出了一种具有“沿流动路径记忆”的扩散-对流过程的新数学模型。这个过程由一个齐次一维狄利克雷初始边界值问题描述,该问题具有沿对流算子特征曲线的分数阶导数。构建并研究了该问题的有限差分近似。证明了有限差分格式的稳定性估计。针对足够平滑的输入数据和解的情况给出了准确度估计。