Results 171 to 180 of about 243,415 (192)

Differential Equations in Banach Algebras

Doklady Mathematics, 2020
In a complex Banach algebra that is not assumed to be commutative, nth-order linear differential equations with constant coefficients are considered. The corresponding algebraic characteristic equation of the nth degree is assumed to have n distinct roots for which the Vandermonde matrix is invertible.
I. D. Kostrub, A. I. Perov
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Differential-Algebraic Systems as Differential Equations on Manifolds [PDF]

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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Differentiation of Constraints in Differential-Algebraic Equations∗

Mechanics of Structures and Machines, 1991
ABSTRACT ABSTRACT Differentiation of constraints that appear in differential-algebraic equations (DAEs) has been advocated for many purposes, ranging from index reduction for numerical purposes to systems inversion in control theory. In this paper, the numerical and analytic consequences of such differentiations are studied and criteria are established
Stephen L. Campbell, Benedict Leimkuhler
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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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Algebraic solutions of algebraic differential equations

Applied Mathematics-A Journal of Chinese Universities, 2005
Using value distribution theory and techniques, the problem of the algebroid solutions of second order algebraic differential equation is investigated. Examples show that the results are sharp.
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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-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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The Lagrange differential-algebraic equations

Journal of Applied Mathematics and Mechanics, 2014
Abstract The Lagrange equations are considered in the case when the Lagrangen function is independent of some of the velocities, and the properties of the differential-algebraic equations arising are studied. It is proved that, when non-degeneracy conditions are satisfied, the equations arising reduce to differential Lagrange equations of lower ...
Ivan I. Kosenko, Alexander A. Burov
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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
Roswitha März, Caren Tischendorf, René Lamour   +2 more
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Nonlinear differential algebraic equations

Siberian Mathematical Journal, 2007
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 an operator transforming the original system to the normal form and prove a general theorem on the ...
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