scholarly journals On the finite dual of a cocommutative Hopf algebroid. Application to linear differential matrix equations and Picard-Vessiot theory.

2021 ◽  
Vol 28 (1) ◽  
Author(s):  
Laiachi El Kaoutit ◽  
José Gómez-Torrecillas
Keyword(s):  
Matrix Equations ◽  
Hopf Algebroid ◽  
Linear Differential ◽  
Differential Matrix

Calculation of the Natural Frequencies of Transverse Vibration of Complex Beams Using the Differential-Matrix Equations

2011 ◽  
Vol 243-249 ◽  
pp. 284-289
Author(s):  
Yu Zhang
Keyword(s):  
Iterative Method ◽  
Boundary Conditions ◽  
Cross Section ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Composite Beams ◽  
Matrix Equations ◽  
Generalized Differential ◽  
Set Up ◽  
Differential Matrix

The generalized differential-matrix equations of transverse vibration of the beams were set up and they were solved by means of Cauchy sequence iterative method. Then according to the boundary conditions at two ends of the beams the natural frequencies of the transverse vibration of the different beams including the complex beams of non-uniform section and composite beams under different boundary conditions were figured out. The form of the differential-matrix is simple. The calculation of the sequence iterations can be accomplished by simple computer program. Using the method in this paper, the amount of work of calculation is reduced greatly and the results are accurate compared with the approximate method in which a beam of non-uniform section is replaced by many small segments of equal cross-section.

An LDLT factorization based ADI algorithm for solving large-scale differential matrix equations

PAMM ◽  
2014 ◽  
Vol 14 (1) ◽  
pp. 827-828 ◽  
Author(s):  
Norman Lang ◽  
Hermann Mena ◽  
Jens Saak
Keyword(s):  
Large Scale ◽  
Matrix Equations ◽  
Differential Matrix

scholarly journals GPU acceleration of splitting schemes applied to differential matrix equations

2019 ◽  
Vol 83 (1) ◽  
pp. 395-419
Author(s):  
Hermann Mena ◽  
Lena-Maria Pfurtscheller ◽  
Tony Stillfjord
Keyword(s):  
Gpu Acceleration ◽  
Matrix Equations ◽  
Splitting Schemes ◽  
Differential Matrix

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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