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

被引：1
作者：
Lapin, Alexander V. V. [1 ,2 ]
Shaydurov, Vladimir V. V. [3 ]
Yanbarisov, Ruslan M. M. [1 ,2 ]
机构：
[1] Sechenov Univ, Moscow 119435, Russia
[2] Russian Acad Sci, Marchuk Inst Numer Math, Moscow 119333, Russia
[3] Russian Acad Sci, Inst Computat Modelling, Siberian Branch, Krasnoyarsk 660036, Russia
来源：
RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING | 2023年 / 38卷 / 01期
基金：
俄罗斯科学基金会;
关键词：
Diffusion-convection equation; quasilinear diffusion operator; variable order fractional material derivative; finite difference scheme; stability; accuracy; ADVECTION-DIFFUSION EQUATION; NUMERICAL-METHODS; ORDER;
D O I：
10.1515/rnam-2023-0003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：23 / 35
页数：13
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