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Semi-explicit DAE

The common underlying principle in the approaches for characterizing the solvability of a DAE system is to obtain, either explicitly, or implicitly, a local representation of an equivalent ODE system, for which available results on existence and uniqueness of solutions are applicable. The derivation of the underlying ODE system involves the repeated differentiation of the algebraic constraints of the DAE, and it is this differentiation process that leads to the concept of a DAE index that is widely used in the literature. For the semi-explicit DAE systems (A. 10) that are of interest to us here, the index has the following definition. [Pg.225]

The index reduced system and the original system have the same solutions if the initial values are consistent. In the case of semi-explicit DAEs this means that the algebraic equations and their derivatives are fulfilled. Then the solution lies in all manifolds defined by the algebraic equations and the overdetermined system... [Pg.164]

First, we consider implicit methods and restrict ourselves to those related to collocation polynomials. For this end we have to extend Definition 4.3.1 to semi-explicit DAEs. [Pg.176]

A brief explanation of differential-algebraic equations (DAE) facilitates a further mathematical discussion of the stagnation-flow equations. In general, DAEs are stated as a vector residual equation, where w is the dependent-variable vector and the prime denotes a time derivative. For the discussion here, it is convenient to consider a restricted class of DAEs called semi-explicit nonlinear DAEs, which are represented as... [Pg.716]

Most of the research on the analysis and numerical simulation of nonlinear DAEs has focused on systems in the fully implicit form of Equation (A.9). However, the generality of the form of the system in Equation (A.9) does not allow the development of explicit controller synthesis results. Also, the majority of chemical process applications (see examples throughout this book), as well as other engineering applications, are modeled by DAEs in a semi-explicit form, such that there is a distinct separation of the differential and algebraic equations ... [Pg.225]

The resulting equations of systems containing algebraic loops can be reduced to a DAE in semi-explicit form ... [Pg.339]

A constrained optimization problem subject to a DAE system, with or without inequality constraints, is referred to as a dynamic optimization problem or optimal control problem. This problem can be posed as follows with the DAEs (14.2 and 14.3) in semi-explicit form ... [Pg.542]

We will rewrite the DAE (5.1.2) in semi-explicit form be introducing an additional variable w... [Pg.152]

We first consider semi-explicit index 1 DAEs of the form... [Pg.259]


See other pages where Semi-explicit DAE is mentioned: [Pg.140]    [Pg.177]    [Pg.140]    [Pg.177]   
See also in sourсe #XX -- [ Pg.140 ]




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