Finite difference scheme for a non-linear subdiffusion problem with a fractional derivative along the trajectory of motion-Reference-Cited by-同舟云学术

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

Published:2023-02-01 Issue:1 Volume:38 Page:23-35
ISSN:1569-3988
Container-title:Russian Journal of Numerical Analysis and Mathematical Modelling
language:en
Short-container-title:

Author:

Lapin Alexander V.¹,Shaydurov Vladimir V.²,Yanbarisov Ruslan M.¹

Affiliation:

1. Sechenov University, Moscow 119435; Marchuk Institute of Numerical Mathematics of Russian Academy of Sciences , Moscow 119333 , Russia

2. Institute of Computational Modelling, Siberian Branch of Russian Academy of Sciences , Krasnoyarsk 660036 , Russia

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Modeling and Simulation,Numerical Analysis

Link

https://www.degruyter.com/document/doi/10.1515/rnam-2023-0003/pdf

Reference15 articles.

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