scholarly journals Analysis and numerical solution of linear delay differential-algebraic equations

2015 ◽  
Vol 56 (2) ◽  
pp. 633-657 ◽  
Author(s):  
Phi Ha ◽  
Volker Mehrmann
Keyword(s):  
Numerical Solution ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Linear Delay ◽  
Delay Differential

scholarly journals Discontinuity Propagation in Delay Differential-Algebraic Equations

2018 ◽  
Vol 34 ◽  
pp. 582-601 ◽  
Author(s):  
Benjamin Unger
Keyword(s):  
Differential Algebraic Equations ◽  
Complete Characterization ◽  
Algebraic Equations ◽  
Case Scenario ◽  
Worst Case ◽  
Linear Delay ◽  
Method Of Steps ◽  
Matrix Pencils ◽  
Delay Differential ◽  
The Impact

The propagation of primary discontinuities in initial value problems for linear delay differential-algebraic equations (DDAEs) is discussed. Based on the (quasi-) Weierstra{\ss} form for regular matrix pencils, a complete characterization of the different propagation types is given and algebraic criteria in terms of the matrices are developed. The analysis, which is based on the method of steps, takes into account all possible inhomogeneities and history functions and thus serves as a worst-case scenario. Moreover, it reveals possible hidden delays in the DDAE and allows to study exponential stability of the DDAE based on the spectral abscissa. The new classification for DDAEs is compared to existing approaches in the literature and the impact of splicing conditions on the classification is studied.

scholarly journals Numerical solution for consistent initial conditions of constrained mechanical systems

2003 ◽  
Vol 25 (3) ◽  
pp. 170-185
Author(s):  
Dinh Van Phong
Keyword(s):  
Numerical Solution ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Differential Algebraic Equations ◽  
System Of Equations ◽  
Algebraic Equations ◽  
Flexible Approach ◽  
Constrained Mechanical Systems ◽  
Consistent Initial Values

The article deals with the problem of consistent initial values of the system of equations of motion which has the form of the system of differential-algebraic equations. Direct treating the equations of mechanical systems with particular properties enables to study the system of DAE in a more flexible approach. Algorithms and examples are shown in order to illustrate the considered technique.

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