A General Class of One-Step Approximation for Index-1 Stochastic Delay-Differential-Algebraic Equations

2019 ◽  
Vol 37 (2) ◽  
pp. 151-169 ◽  
Author(s):  
Tingting Qin and Chengjian Zhang
Keyword(s):  
General Class ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Stochastic Delay ◽  
Step Approximation ◽  
One Step ◽  
Delay Differential

scholarly journals The Pantelides algorithm for delay differential-algebraic equations

2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Ines Ahrens ◽  
Benjamin Unger
Keyword(s):  
Differential Algebraic Equations ◽  
Equivalence Classes ◽  
Point Of View ◽  
Algebraic Equations ◽  
Sufficient Criterion ◽  
Differential Algebraic Equation ◽  
Graph Theoretical Approach ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Structural Point

Abstract We present a graph-theoretical approach that can detect which equations of a delay differential-algebraic equation (DDAE) need to be differentiated or shifted to construct a solution of the DDAE. Our approach exploits the observation that differentiation and shifting are very similar from a structural point of view, which allows us to generalize the Pantelides algorithm for differential-algebraic equations to the DDAE setting. The primary tool for the extension is the introduction of equivalence classes in the graph of the DDAE, which also allows us to derive a necessary and sufficient criterion for the termination of the new algorithm.

scholarly journals Boundary Criteria for the Stability of Delay Differential-Algebraic Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Leping Sun ◽  
Yuhao Cong
Keyword(s):  
Asymptotic Stability ◽  
Differential Algebraic Equations ◽  
Analytical Function ◽  
Algebraic Equations ◽  
Stability Criteria ◽  
Stability Regions ◽  
The Stability ◽  
Delay Differential

This paper is concerned with the asymptotic stability of delay differential-algebraic equations. Two stability criteria described by evaluating a corresponding harmonic analytical function on the boundary of a certain region are presented. Stability regions are also presented so as to show the method geometrically. Our results are not reported.

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