Results 271 to 280 of about 12,855 (288)

Algebraic Differential Equations

2017
One of the most difficult problems in the theory of Algebraic Differential Equations is to decide whether or not the solutions are meromorphic in the plane. In case this question has been answered satisfactorily, which by experience requires particular strategies adapted to the equations under consideration, there remain several major problems to be ...
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Index-2 Differential-Algebraic Equations

Results in Mathematics, 1989
A class of general nontransferable differential-algebraic equations which contains all linear differential-algebraic equations having the global index 2 in the definition of Gear and Petzold or being tractable with index 2 in the sense of Griepentrog and März as well as nonlinear index-2 equations in the understanding of Brenan, Gear, Petzold and ...
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Differential-Algebraic Equations: A Tutorial Review

International Journal of Bifurcation and Chaos, 1998
This article (Funded by EPSRC and the National Grid Company.) explores some introductory principles of differential-algebraic equations (DAEs) and makes a connection with the theory of dynamical systems. Some results which are new in the field of DAEs are also surveyed.
Beardmore, R. E., Song, Y. H.
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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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Solvability of General Differential Algebraic Equations

SIAM Journal on Scientific Computing, 1995
Summary: 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.
Campbell, Stephen L., Griepentrog, E.
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Differential-Algebraic Equations

1984
In this paper we study the numerical solution of the differential/algebraic systems F(t, y, y′) = 0. Many of these systems can be solved conveniently and economically using a range of ODE methods. Others can be solved only by a small subset of ODE methods, and still others present insurmountable difficulty for all current ODE methods.
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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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Abstract differential-algebraic equations

2013
The concept of regular DAEs developed in Part I for DAEs in finite-dimensional spaces is generalized to some extend for DAEs acting in Hilbert spaces, which are called abstract differential-algebraic equations (ADAEs). Such a framework aims to provide a systematic approach for coupled systems of different type. It should be emphasized that this working
René Lamour, Roswitha März, Caren Tischendorf   +2 more
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Nonlinear differential algebraic equations

Siberian Mathematical Journal, 2007
Summary: We consider a system of nonlinear ordinary differential equations that are not solved with respect to the derivative of the unknown vector function and degenerate identically in the domain of definition. We obtain conditions for the existence of a map transforming the original system to the normal form and prove a general theorem on the ...
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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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