Метод конечных разностей для уравнения переноса с распределенными параметрами на сети
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Научный журнал Моделирование, оптимизация и информационные технологииThe scientific journal Modeling, Optimization and Information Technology
Online media
issn 2310-6018

Finite difference method for transfer equation with distributed parameters on the network

Tran D.   idProvotorov V.V.

UDC УДК 517.977.56
DOI: 10.26102/2310-6018/2021.34.3.012

  • Abstract
  • List of references
  • About authors

The issue of constructing a solution to an initial-boundary value problem for an evolutionary differential equation with a spatial variable varying on a network (geometric graph) has remained under review of researchers over the past few years. There were many practical reasons for this - a large number of mathematical models describing the transport processes of continuous media over network carriers use formalisms of partial differential equations and their corresponding initial-boundary value problems. In this paper, classical approaches were used for approximating differential equations on linear network fragments (graph edges), and the principles of constructing approximations of differential relations generated by generalized Kirchhoff conditions at the junction points of these fragments (at the graph nodes) were also indicated. The latter was a distinctive feature of differential equations concept with a spatial variable, changing on a network (graph) and its corresponding finite-difference analogue of the classical equation and finite-difference analogue. The problems of the elliptic operator approximation of the initial-boundary value problem were studied (the error of approximations was established), the stability of the two-layer difference scheme and detailed analysis of its stability was carried out. An algorithm for constructing a solution was developed, based on new numerical methods for analyzing transport problems in materials with complex structure with non-uniformly distributed properties of a continuous medium over a network carrier. A computer program has been developed and tested on test objectives targeted at applied problems. The obtained results can be used in the analysis of initial-boundary value problems for differential equations with distributed parameters on a multidimensional network having interesting analogies with multiphase problems in multidimensional hydrodynamics.

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Tran Duy

Email: tranduysp94@gmail.com

Voronezh State University, Voronezh, Russian Federation

Voronezh, Russia

Provotorov Vyacheslav Vasil’evich
Dr. Sci. in Physics and Mathematics, associate professor
Email: wwprov@mail.ru

ORCID |

Voronezh State University, Voronezh, Russian Federation

Voronezh, Russia

Keywords: initial-boundary value transfer problem, network (directed graph), weak solution, finite-dimensional analogue of differential operators, stability of difference schemes

For citation: Tran D. Provotorov V.V. Finite difference method for transfer equation with distributed parameters on the network. Modeling, Optimization and Information Technology. 2021;9(3). Available from: https://moitvivt.ru/ru/journal/pdf?id=1019 DOI: 10.26102/2310-6018/2021.34.3.012 (In Russ).

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Full text in PDF

Received 14.07.2021

Revised 16.09.2021

Accepted 23.09.2021

Published 30.09.2021