Bazylevych Y.N., Kostiushko I.A., Stanina O.D.
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 simplify the problem significantly and obtain an analytical solution in many cases. © 2023, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: decomposition, matrices, partial differential equations, similarity transformations, Decomposition, Linear transformations, Partial differential equations, Algebraic method, Block diagonal, Block triangular forms, Coefficient matrix, Decomposition methods, First order partial differential equations, matrix, Sequential decomposition, Similarity transformation, Systems of equations, Matrix algebra

Cite:
Bazylevych Y.N., Kostiushko I.A., Stanina O.D. (2023). Solving a system of first-order partial differential equations using decomposition methods. Cybernetics and Systems Analysis, 59 (3), 127–132. doi: https://doi.org/10.1007/s10559-023-00581-3 http://jnas.nbuv.gov.ua/article/UJRN-0001402515 [In Ukrainian].