Higher order matrix differential equations with singular coefficient matrices

2015 ◽  
Author(s):  
V. C. Fragkoulis ◽  
I. A. Kougioumtzoglou ◽  
A. A. Pantelous ◽  
A. Pirrotta
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
Singular Coefficient ◽  
Order Matrix ◽  
Matrix Differential Equations ◽  
Matrix Differential

scholarly journals On the Approximated Solution of a Special Type of Nonlinear Third-Order Matrix Ordinary Differential Problem

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2262
Author(s):  
Emilio Defez ◽  
Javier Ibáñez ◽  
José M. Alonso ◽  
Michael M. Tung ◽  
Teresa Real-Herráiz
Keyword(s):  
Differential Equations ◽  
Numerical Test ◽  
Test Problems ◽  
Science And Engineering ◽  
Third Order ◽  
Differential Problem ◽  
Order Matrix ◽  
Engineering Problems ◽  
Matrix Differential Equations ◽  
Matrix Differential

Matrix differential equations are at the heart of many science and engineering problems. In this paper, a procedure based on higher-order matrix splines is proposed to provide the approximated numerical solution of special nonlinear third-order matrix differential equations, having the form Y(3)(x)=f(x,Y(x)). Some numerical test problems are also included, whose solutions are computed by our method.

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.

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