A diffusion–convection problem with a fractional derivative along the trajectory of motion-Reference-Cited by-同舟云学术

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

Published:2021-06-01 Issue:3 Volume:36 Page:157-163
ISSN:1569-3988
Container-title:Russian Journal of Numerical Analysis and Mathematical Modelling
language:en
Short-container-title:

Author:

Lapin Alexander V.¹²,Shaidurov Vladimir V.²³

Affiliation:

1. Sechenov University , Moscow , Russia

2. Coordinated Innovation Center for Computable Modeling in Management Science, Tianjin University of Finance and Economics , Tianjin , P. R. China

3. Institute of Computational Modelling, Siberian Branch of Russian Academy of Sciences , Krasnoyarsk , Russia

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Modelling and Simulation,Numerical Analysis

Link

https://www.degruyter.com/document/doi/10.1515/rnam-2021-0013/pdf

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