scholarly journals Legendre Neural Network for Solving Linear Variable Coefficients Delay Differential-Algebraic Equations with Weak Discontinuities

2021 ◽  
Vol 13 (1) ◽  
pp. 101-118
Author(s):  
global sci
Keyword(s):  
Neural Network ◽  
Variable Coefficients ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Weak Discontinuities ◽  
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.

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