Results 181 to 190 of about 387,114 (225)

Ordinary Differential Equations

1994
Dynamical systems are often expressed in terms of ordinary differential equations. An example are the canonical equations of motion in Hamiltonian systems $${\dot p_i} = - \frac{{\partial H}}{{\partial {q_i}}},\;{\dot p_i} = \frac{{\partial H}}{{\partial {q_i}}},$$ (12.1) where the time derivatives of the canonical coordinates and momenta are
H.-J. Jodl, H. J. Korsch
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Ordinary differential equations

2010
A differential equation is an equation involving one or more derivatives of an unknown function. If all derivatives are taken with respect to a single independent variable we call it an ordinary differential equation, whereas we have a partial differential equation when partial derivatives are present.
Fausto Saleri, Alfio Quarteroni, Alfio Quarteroni, Paola Gervasio   +3 more
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Explicit Ordinary Differential Equations [PDF]

, 1998
In the last chapter we discussed the numerical treatment of explicit ordinary differential equations. Here, we will consider the more general case, implicit ordinary differential equations.
Edda Eich-Soellner, Claus Führer
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Ordinary Differential Equations

1978
Linear differential equations with constant coefficients are an important area of application of the Laplace transform. As a prelude to the discussion of such problems we discuss first two particularly simple examples, since the connection with the classical methods of solution is readily apparent in these cases.
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Ordinary differential equations

2015
A large part of the natural phenomena occurring in physics, engineering and other applied sciences can be described by a mathematical model, a collection of relations involving a function and its derivatives.
Anita Tabacco, Claudio Canuto
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Ordinary Differential Equations [PDF]

, 1983
We link here directly with the shrinking lemma, and this section may be read immediately after the first section of the preceding chapter.
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Multivalued Differential Equations and Ordinary Differential Equations

SIAM Journal on Applied Mathematics, 1970
(E) e F(x, t), where F is upper semicontinuous, from known results in the theory of ordinary differential equations. This will be accomplished by showing that, for any F upper semicontinuous and convex, it is always possible to "approximate" the multivalued differential equation (E) by appropriately chosen ordinary differential equations. This would be
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Differential Equations: Ordinary

2000
There is no more useful tool for the study of differential equations, in particular if they are in two dimensions, than the phase portrait. Many important systems both in physics and in economics in fact live in two dimensions. All second order systems are two dimensional.
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Attractors of Ordinary Differential Equations

Ukrainian Mathematical Journal, 2000
The author gives sufficient conditions for the existence of polynomial attractors for ODEs. This problem is generally treated by perturbation techniques. Here, the author uses Lyapunov vector functions and introduces the notion of polynomial asymptotic equilibrium.
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Ordinary Differential Equations

1970
The numerical treatment of ordinary differential equations is a field whose scope has broadened quite a bit over the last 50 years. In particular, a whole spectrum of different stability conditions has developed. Since this chapter is not the place to present all details, we concentrate on the most basic concept of stability.
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