Solving a System of First-Order Partial Differential Equations Using Decomposition Methods

The paper describes simplifying a system of equations by decomposing it into independent subsystems or by hierarchical (sequential) decomposition. The authors have developed algebraic methods for transforming coefficient matrices into block-diagonal or block-triangular forms. They allow one to simpl...

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Bibliographic Details
Published inCybernetics and systems analysis Vol. 59; no. 3; pp. 467 - 472
Main Authors Bazylevych, Y. N., Kostiushko, I. A., Stanina, O. D.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.05.2023
Springer
Springer Nature B.V
Subjects
Analysis
Artificial Intelligence
Control
Decomposition
Differential equations
Exact solutions
Mathematical analysis
Mathematics
Mathematics and Statistics
Methods
Partial differential equations
Processor Architectures
Software Engineering/Programming and Operating Systems
Subsystems
Systems Theory
decomposition
partial differential equations
matrices
similarity transformations
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Summary:The paper describes simplifying a system of equations by decomposing it into independent subsystems or by hierarchical (sequential) decomposition. The authors have developed algebraic methods for transforming coefficient matrices into block-diagonal or block-triangular forms. They allow one to simplify the problem significantly and obtain an analytical solution in many cases.
ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-023-00581-3