沿运动轨迹具有分数导数的非线性次扩散问题的有限差分格式

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2023-02-01 DOI:10.1515/rnam-2023-0003

A. Lapin, V. Shaydurov, R. Yanbarisov

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引用次数: 1

摘要

摘要考虑对流算子的特征，构造并研究了一类具有分数阶导数的一维扩散对流方程的有限差分格式。它在以下方面发展了前人[5,6]的结果:微分方程包含一个沿对流算子和拟线性扩散算子特征的变阶分数阶导数;提出了一种新的精度估计方法，该方法排除了网格格式精度对特征曲率的依赖关系。

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Finite difference scheme for a non-linear subdiffusion problem with a fractional derivative along the trajectory of motion

Abstract The article is devoted to the construction and study of a finite-difference scheme for a one-dimensional diffusion–convection equation with a fractional derivative with respect to the characteristic of the convection operator. It develops the previous results of the authors from [5, 6] in the following ways: the differential equation contains a fractional derivative of variable order along the characteristics of the convection operator and a quasi-linear diffusion operator; a new accuracy estimate is proved, which singles out the dependence of the accuracy of mesh scheme on the curvature of the characteristics.

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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.