Results 251 to 260 of about 245,826 (285)

Differential-Algebraic Equations

Oberwolfach Reports, 2007
The 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, Roswitha März, Linda Petzold, Peter Rentrop   +3 more
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Solutions of Linear Differential Algebraic Equations

SIAM Review, 1998
Summary: The authors show how to solve inhomogeneous linear differential algebraic systems with constant coefficients.
Mazi Shirvani, Joseph W.-H. So
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Differential Algebraic Equations

2017
This 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, Carl D. Laird, Jean-Paul Watson, David L. Woodruff, Gabriel A. Hackebeil, Bethany L. Nicholson, John D. Siirola   +6 more
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Differential — Algebraic Equations

2003
Differential — 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

2004
Asymptotics 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 Equations in Algebras

2008
The 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

2012
In 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, Jeff Cash, Francesca Mazzia   +2 more
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Differential-Algebraic Equations

2016
In 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, G. Alì, W. H. A. Schilders   +2 more
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Differential-Algebraic Systems as Differential Equations on Manifolds

Mathematics of Computation, 1984
Based on the theory of differential equations on manifolds, existence and uniqueness results are proved for a class of mixed systems of differential and algebraic equations as they occur in various applications. Both the autonomous and nonautonomous case are considered.
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Algebraic solutions of algebraic differential equations

Applied Mathematics-A Journal of Chinese Universities, 2005
The author gives a condition under which a second-order algebraic differential equation has an algebraic solution. Let \(a_0\dots, a_p\), \(b_0,\dots, q\) be nonzero entire functions of one variable such that they have a finite number of poles and without common zero, and consider the following equation: \[ (w'')^n= \Biggl(\sum^p_{i=0} a_i(z) w^i\Biggr)
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