Stability of the weighted splitting finite-difference scheme for a two-dimensional parabolic equation with two nonlocal integral conditions

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Nonlocal conditions arise in mathematical models of various physical, chemical or biological processes. Therefore, interest in developing computational techniques for the numerical solution of partial differential equations (PDEs) with various types of nonlocal conditions has been growing fast. We construct and analyse a weighted splitting finitedifference scheme for a two-dimensional parabolic equation with nonlocal integral conditions. The main attention is paid to the stability of the method. We apply the stability analysis technique which is based on the investigation of the spectral structure of the transition matrix of a finite-difference scheme. We demonstrate that depending on the parameters of the finite-difference scheme and nonlocal conditions the proposed method can be stable or unstable. The results of numerical experiments with several test problems are also presented and they validate theoretical results.
Original languageEnglish
Pages (from-to)3485-3499
JournalComputers and Mathematics with Applications
Volume64
Issue number11
DOIs
Publication statusPublished - 2012

Fingerprint

Integral Condition
Nonlocal Conditions
Finite Difference Scheme
Parabolic Equation
Partial differential equations
Mathematical models
Computational Techniques
Transition Matrix
Test Problems
Stability Analysis
Partial differential equation
Experiments
Unstable
Numerical Experiment
Numerical Solution
Mathematical Model
Demonstrate

Keywords

  • Parabolic equation
  • Nonlocal integral conditions
  • Weighted splitting finite-difference scheme
  • Stability

Cite this

@article{27818ef46f8d4f99ba7c40f890399c34,
title = "Stability of the weighted splitting finite-difference scheme for a two-dimensional parabolic equation with two nonlocal integral conditions",
abstract = "Nonlocal conditions arise in mathematical models of various physical, chemical or biological processes. Therefore, interest in developing computational techniques for the numerical solution of partial differential equations (PDEs) with various types of nonlocal conditions has been growing fast. We construct and analyse a weighted splitting finitedifference scheme for a two-dimensional parabolic equation with nonlocal integral conditions. The main attention is paid to the stability of the method. We apply the stability analysis technique which is based on the investigation of the spectral structure of the transition matrix of a finite-difference scheme. We demonstrate that depending on the parameters of the finite-difference scheme and nonlocal conditions the proposed method can be stable or unstable. The results of numerical experiments with several test problems are also presented and they validate theoretical results.",
keywords = "Parabolic equation, Nonlocal integral conditions, Weighted splitting finite-difference scheme, Stability",
author = "Svajūnas Sajavičius",
year = "2012",
doi = "10.1016/j.camwa.2012.08.009",
language = "English",
volume = "64",
pages = "3485--3499",
journal = "Computers and Mathematics with Applications",
issn = "0898-1221",
publisher = "Elsevier Limited",
number = "11",

}

TY - JOUR

T1 - Stability of the weighted splitting finite-difference scheme for a two-dimensional parabolic equation with two nonlocal integral conditions

AU - Sajavičius, Svajūnas

PY - 2012

Y1 - 2012

N2 - Nonlocal conditions arise in mathematical models of various physical, chemical or biological processes. Therefore, interest in developing computational techniques for the numerical solution of partial differential equations (PDEs) with various types of nonlocal conditions has been growing fast. We construct and analyse a weighted splitting finitedifference scheme for a two-dimensional parabolic equation with nonlocal integral conditions. The main attention is paid to the stability of the method. We apply the stability analysis technique which is based on the investigation of the spectral structure of the transition matrix of a finite-difference scheme. We demonstrate that depending on the parameters of the finite-difference scheme and nonlocal conditions the proposed method can be stable or unstable. The results of numerical experiments with several test problems are also presented and they validate theoretical results.

AB - Nonlocal conditions arise in mathematical models of various physical, chemical or biological processes. Therefore, interest in developing computational techniques for the numerical solution of partial differential equations (PDEs) with various types of nonlocal conditions has been growing fast. We construct and analyse a weighted splitting finitedifference scheme for a two-dimensional parabolic equation with nonlocal integral conditions. The main attention is paid to the stability of the method. We apply the stability analysis technique which is based on the investigation of the spectral structure of the transition matrix of a finite-difference scheme. We demonstrate that depending on the parameters of the finite-difference scheme and nonlocal conditions the proposed method can be stable or unstable. The results of numerical experiments with several test problems are also presented and they validate theoretical results.

KW - Parabolic equation

KW - Nonlocal integral conditions

KW - Weighted splitting finite-difference scheme

KW - Stability

U2 - 10.1016/j.camwa.2012.08.009

DO - 10.1016/j.camwa.2012.08.009

M3 - Article

VL - 64

SP - 3485

EP - 3499

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 11

ER -