Results 281 to 289 of about 12,657 (289)

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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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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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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Analytic Solutions of Algebraic Differential Equations

SIAM Journal on Mathematical Analysis, 1979
For special polynomials $f_2 (w)$, $f_1 (w)$, $f_0 (w)$ in w with analytic coefficients, the equation $f_2 (w)w'^2 + f_1 (w)w' + f_0 (w) = 0$ has appeared many times in the literature. Frequently, the equation is irreducible, $\deg f_2 = 0$, $\deg f_1 \leqq 2$, $\deg f_0 \leqq 4$, and either $4f_2 f_0 - f_1^2 $ has a multiple root or its degree is ...
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Regularizations of Differential‐Algebraic Equations Revisited

Mathematische Nachrichten, 1995
AbstractThe present paper deals with quasilinear differential‐algebraic equations with index 2. These equations are approximated by regularization methods. Such methods lead to singularly perturbed differential‐algebraic equations. Using a geometric theory of singular perturbations convergence of the solutions of the regularized problems towards that ...
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Explicit Differential-Algebraic Equations

2020
Federico Milano, Ioannis Dassios, Muyang Liu, Georgios Tzounas   +3 more
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Algebraic differential equations

2006
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Polynomial solutions for algebraic differential equations

Lazov, P., Dimitrovskij, D. N.
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