Hybrid systems of differential-algebraic equations – Analysis and numerical solution

2009 ◽  
Vol 19 (8) ◽  
pp. 1218-1228 ◽  
Author(s):  
Volker Mehrmann ◽  
Lena Wunderlich
Keyword(s):  
Numerical Solution ◽  
Hybrid Systems ◽  
Differential Algebraic Equations ◽  
Algebraic Equations

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.

scholarly journals Sensitivity Analysis for Hybrid Systems and Systems With Memory

2019 ◽  
Vol 14 (9) ◽  
Author(s):  
Radu Serban ◽  
Antonio Recuero
Keyword(s):  
Hybrid Systems ◽  
Exponential Model ◽  
Differential Algebraic Equations ◽  
Mode Switching ◽  
Continuous Systems ◽  
Algebraic Equations ◽  
Adjoint Sensitivity ◽  
Adjoint Systems ◽  
Systems With Memory ◽  
With Memory

We present an adjoint sensitivity method for hybrid discrete—continuous systems, extending previously published forward sensitivity methods (FSA). We treat ordinary differential equations (ODEs) and differential-algebraic equations (DAEs) of index up to two (Hessenberg) and provide sufficient solvability conditions for consistent initialization and state transfer at mode switching points, for both the sensitivity and adjoint systems. Furthermore, we extend the analysis to so-called hybrid systems with memory where the dynamics of any given mode depend explicitly on the states at the last mode transition point. We present and discuss several numerical examples, including a computational mechanics problem based on the so-called exponential model (EM) constitutive material law for steel reinforcement under cyclic loading.

The numerical solution of differential-algebraic equations by sinc-collocation method

2013 ◽  
Vol 32 (2) ◽  
pp. 343-354 ◽  
Author(s):  
Somayeh Yeganeh ◽  
Abbas Saadatmandi ◽  
Fahimeh Soltanian ◽  
Mehdi Dehghan
Keyword(s):  
Numerical Solution ◽  
Collocation Method ◽  
Differential Algebraic Equations ◽  
Algebraic Equations
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