scholarly journals Matrix differential equations and scalar polynomials satisfying higher order recursions

2009 ◽  
Vol 354 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Antonio J. Durán ◽  
F. Alberto Grünbaum
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
Matrix Differential Equations ◽  
Matrix Differential

SIGNS OF REGULARITY AND STABILITY OF DIFFERENTIAL EQUATIONS OF HIGHER ORDER

2018 ◽  
pp. 674-678
Author(s):  
Anatoly Ivanovich Perov ◽  
Irina Dmitrievna Kostrub
Keyword(s):  
Differential Equations ◽  
Main Part ◽  
Higher Order ◽  
Matrix Differential Equations ◽  
Matrix Differential ◽  
Vector Matrix

On the basis of previous works of authors new signs of regularity and stability of vector-matrix differential equations with a variable main part are specified.

scholarly journals Solutions of Higher-Order Homogeneous Linear Matrix Differential Equations for Consistent and Non-Consistent Initial Conditions: Regular Case

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Ioannis K. Dassios
Keyword(s):  
Differential Equations ◽  
Initial Conditions ◽  
Matrix Pencil ◽  
Higher Order ◽  
Linear Matrix ◽  
Regular Case ◽  
Numerical Examples ◽  
Matrix Differential Equations ◽  
Matrix Differential ◽  
Homogeneous Linear

We study a class of linear matrix differential equations (regular case) of higher order whose coefficients are square constant matrices. By using matrix pencil theory and the Weierstrass canonical form of the pencil we obtain formulas for the solutions and we show that the solution is unique for consistent initial conditions and infinite for nonconsistent initial conditions. Moreover we provide some numerical examples. These kinds of systems are inherent in many physical and engineering phenomena.

On differential equations in Banach algebras

2020 ◽  
pp. 410-421
Author(s):  
Anatoly I. Perov ◽  
Irina D. Kostrub
Keyword(s):  
Differential Equations ◽  
Banach Algebras ◽  
Higher Order ◽  
Original Research ◽  
Matrix Equations ◽  
Small Oscillations ◽  
Matrix Differential Equations ◽  
Constant Coefficients ◽  
Linear Differential ◽  
Matrix Differential

We consider higher-order linear differential equations with constant coefficients in Banach algebras (this is a direct generalization of higher-order matrix differential equations). The presentation is based on higher algebra, differential equations and functional analysis. The results obtained can be used in the study of matrix equations, in the theory of small oscillations in physics, and in the theory of perturbations in quantum mechanics. The presentation is based on the original research of the authors.

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