Method of lines for reaction-diffusion systems admitting invariant regions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F25%3A00388524" target="_blank" >RIV/68407700:21340/25:00388524 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.14311/AP.2025.65.0566" target="_blank" >https://doi.org/10.14311/AP.2025.65.0566</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.14311/AP.2025.65.0566" target="_blank" >10.14311/AP.2025.65.0566</a>
Alternative languages
Result language
angličtina
Original language name
Method of lines for reaction-diffusion systems admitting invariant regions
Original language description
Systems of nonlinear reaction-diffusion equations arise in various fields, including chemistry, population dynamics, pattern formation, phase transitions, and image processing. With the exception of few analytically solvable cases, they are treated by numerical methods carefully adjusted to capture the nonlinear phenomena exhibited by the solution. This article shows how to extend the notion of invariant regions generalizing the maximum principle for diffusion equations to the finite-difference method of lines, and how to consequently prove convergence of the underlying numerical scheme. We also provide two particular examples of reaction-diffusion systems in one-dimensional space with a diagonal diffusion operator, which are solved by the presented numerical method.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA25-18265S" target="_blank" >GA25-18265S: Computational models of hydraulic fracturing in geothermal energy production</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Acta Polytechnica
ISSN
1210-2709
e-ISSN
1805-2363
Volume of the periodical
65
Issue of the periodical within the volume
5
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
12
Pages from-to
566-577
UT code for WoS article
001625343400009
EID of the result in the Scopus database
2-s2.0-105023276780