沿运动轨迹具有分数导数的扩散-对流问题

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2021-06-01 DOI:10.1515/rnam-2021-0013

A. Lapin, V. Shaidurov

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引用次数: 4

摘要

摘要提出了一种新的具有“沿流路记忆”的扩散-对流过程数学模型。该过程由一个沿对流算子特征曲线的分数阶导数的齐次一维Dirichlet初边值问题描述。构造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。给出了输入数据足够平滑的情况下的精度估计和解决方案。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A diffusion–convection problem with a fractional derivative along the trajectory of motion

Abstract 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.

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来源期刊

Russian Journal of Numerical Analysis and Mathematical Modelling 数学-工程：综合

CiteScore

1.40

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： The Russian Journal of Numerical Analysis and Mathematical Modelling, published bimonthly, provides English translations of selected new original Russian papers on the theoretical aspects of numerical analysis and the application of mathematical methods to simulation and modelling. The editorial board, consisting of the most prominent Russian scientists in numerical analysis and mathematical modelling, selects papers on the basis of their high scientific standard, innovative approach and topical interest. Topics: -numerical analysis- numerical linear algebra- finite element methods for PDEs- iterative methods- Monte-Carlo methods- mathematical modelling and numerical simulation in geophysical hydrodynamics, immunology and medicine, fluid mechanics and electrodynamics, geosciences.