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Solvability of General Differential Algebraic Equations
SIAM Journal on Scientific Computing, 1995Summary: In the last few years there has been considerable research on differential algebraic equations (DAE) \(f(t,x,x') = 0\) where \(f_{x'}\) is identically singular. Most of this effort has focused on computing a solution that is assumed to exist. That is, the DAE is assumed solvable.
Stephen L. Campbell, E. Griepentrog
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Solutions of Linear Differential Algebraic Equations
SIAM Review, 1998Summary: The authors show how to solve inhomogeneous linear differential algebraic systems with constant coefficients.
Mazi Shirvani, Joseph W.-H. So
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Sensitivity analysis of differential-algebraic equations and partial differential equations [PDF]
Computers and Chemical Engineering, 2006 Sensitivity analysis generates essential information for model development, design optimization, parameter estimation, optimal control, model reduction and experimental design. In this paper we describe the forward and adjoint methods for sensitivity analysis, and outline some of our recent work on theory, algorithms and software for sensitivity ...
Linda Petzold +2 more
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Differential-Algebraic Equations
Oberwolfach Reports, 2007The topic of Differential Algebraic Equations (DAEs) began to attract significant research interest in applied and numerical mathematics in the early 1980's. Today, a quarter of a century later, DAEs are an independent field of research, which is gaining in importance and becoming of increasing interest for both applications and mathematical theory.
Stephen L. Campbell +3 more
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Differential Algebraic Equations
2017This chapter documents how to formulate and solve optimization problems with differential and algebraic equations (DAEs). The pyomo.dae package allows users to easily incorporate detailed dynamic models within an optimization framework and is flexible enough to represent a wide variety of differential equations.
William E. Hart +6 more
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Differential — Algebraic Equations
2003Differential — algebraic equations (DAE) differ from other problems with solutions given by smooth and continuous parametric sets. They combine specifics of the nonlinear algebraic or transcendental equations with those of ODE. Correct formulation of the Cauchy problem for such equations requires solution of a system of nonlinear equations.
V. I. Shalashilin, E. B. Kuznetsov
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Algebraic Differential Equations
2004Asymptotics have been much used in the study of differential equations. The method of undetermined coefficients is one common technique. At its most basic, this consists of substituting a general power series into the equation and then comparing terms in order to find the coefficients.
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Differential Algebraic Equations
2012In Chaps. 2 and 3 we were concerned mainly with the numerical solution of ordinary differential equations of the form y′ = f(x, y). However, there are problems which are more general than this and require special methods for their solution. One such class of problems are differential algebraic equations (DAEs).
Karline Soetaert +2 more
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Differential Equations in Algebras
2008The aim of this work is to investigate how topological and dynamical properties of differential equations (in the sequel DE) are reflected in the associated algebras, as well as to show how basic algebraic concepts provide valuable insights in DE.
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Differential-Algebraic Equations
2016In this chapter, we introduce the differential algebraic equations which we abbreviate as DAEs. DAEs arise in a variety of applications such as modelling constrained multibody systems, electrical networks, aerospace engineering, chemical processes, computational fluid dynamics, gas transport networks, see [10–12, 35].
N. Banagaaya +2 more
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