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Explicit Differential-Algebraic Equations
Published in Federico Milano, Ioannis Dassios, Muyang Liu, Georgios Tzounas, Eigenvalue Problems in Power Systems, 2020
Federico Milano, Ioannis Dassios, Muyang Liu, Georgios Tzounas
In mathematics, differential-algebraic equations (DAEs) are a system of equations that either contains differential equations and algebraic equations, or is equivalent to such a system. Such systems occur as the general form of systems of differential equations for vector-valued functions x in one independent variable t. Overall differential-algebraic equations have the following singular non-linear form: EIξ.=φ(ξ),
Three-Dimensional Dynamic Anatomical Modeling of the Human Knee Joint
Published in Cornelius Leondes, Musculoskeletal Models and Techniques, 2001
Mohamed Samir Hefzy, Eihab Muhammed Abdel-Rahman
where y→=dy→dt and y→=dy→dt. This system has two parts: a differential part and an algebraic part. These ODE systems are called differential-algebraic equations (DAEs). Numerical methods from the field of ODEs have classically been employed to solve DAE systems.24,53–56,105
Ordinary differential equations
Published in Victor A. Bloomfield, Using R for Numerical Analysis in Science and Engineering, 2018
Differential algebraic equations (DAEs) contain a combination of ODEs, which are responsible for the evolution of the system, and algebraic equations, which impose constraints on the solution. Common examples arise in chemical reaction kinetics, where differential equations describe the time variation of the concentrations of the chemical species, while equilibrium or conservation equations constrain the allowable values of the concentrations.
An algorithm to modify consistent initialization of differential-algebraic equations obtained by pantelides algorithm using minimally singular subsets
Published in SICE Journal of Control, Measurement, and System Integration, 2021
Keisuke Shimako, Masanobu Koga
A Differential Algebraic Equation (DAE) is a system of ordinary differential equations (ODE) and algebraic equations. ODEs often appear to describe phenomena in the fields such as science, engineering, and economics. Algebraic equations represent constraints that must be satisfied for phenomena. Since theories regarding DAEs have attracted more recent attention in comparison with that of ODE, they are in a state of flux [1]. The DAE system is usually solved by approximating DAE to ODE. However, it has been required to solve the DAE without approximation with software tools.
How AD can help solve differential-algebraic equations
Published in Optimization Methods and Software, 2018
John D. Pryce, Nedialko S. Nedialkov, Guangning Tan, Xiao Li
Many numerical methods for higher index DAEs start with index reduction: augmenting the DAE by time-derivatives of some of its equations to produce a DAE of larger size and smaller index. Various index reduction methods have been used that convert the DAE to an ODE with more degrees of freedom than the DAE. Then the DAE's solution paths form a proper subset of those of the ODE. This tends to be bad numerically, as errors cause drift from the consistent manifold that can be exponential once it starts.