Results 181 to 190 of about 250,459 (212)

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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Explicit Differential-Algebraic Equations

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

1996
Necessary conditions for the Newton polygon associated with a general differential equation algebraic in the unknown function and its Schwarzian derivative are presented in the case of existence of an admissible solution (in Nevanlinna sense). Moreover, an admissible solution is shown to satisfy a stronger version of Nevanlinna's defect relation.
Hotzel, Richard, Jank, Gerhard
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Solving integral equations in free space with inverse-designed ultrathin optical metagratings

Nature Nanotechnology, 2023
Andrea Cordaro, Andrea Alu
exaly  

DeepXDE: A Deep Learning Library for Solving Differential Equations

SIAM Review, 2021
Lu Lu, George E Karniadakis
exaly