Results 261 to 270 of about 52,901 (306)

Explicit Ordinary Differential Equations

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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On Implicit Ordinary Differential Equations

IMA Journal of Numerical Analysis, 1984
A geometric analysis of the problem \(f(x,y,y')=0\) is given which may be of value in developing numerical methods for solution near the singular points where \(fy'=0\). In particular, the approach here shows problems of switching branches when computing numerically a solution near an envelope, as noted by \textit{L. Fox} and \textit{D. F.
A. JEPSON, A. SPENCE
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Uniqueness for ordinary differential equations

Mathematical Systems Theory, 1975
Various criteria are known for assuring uniqueness of the solution of a system ofn ordinary differential equations,x′ = f(t, x), with initial conditionx(t0) = x0. Most of these involve some sort of relaxed Lipschitz condition onf(t, x), with respect tox, valid on an open setD ⊂ R1+n which contains the point (t0, x0).
Stephen R. Bernfeld, Rodney D. Driver, V. Lakshmikantham   +2 more
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Reducible Ordinary Differential Equations

Journal of Nonlinear Science, 2006
The class of reducible differential equations under consideration here includes the class of symmetric systems, and examples show that the inclusion is proper. We first discuss reducibility, as well as the stronger concept of complete reducibility, from the viewpoint of Lie algebras of vector fields and their invariants, and find Lie algebra conditions
Karl Peter Hadeler, Sebastian Walcher
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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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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 in Rn

1984
We see that numerous applications to biology, chemistry, economics and medicine have recently been added to the traditional ones in mechanics, hence ordinary differential equations become again a fundamental tool for understanding scientific world. In the last yeares interest for non linear analysis has steadily grown, and the theory of non linear ...
PICCININI, Livio Clemente, STAMPACCHIA G, VIDOSSICH G.   +2 more
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Ordinary Differential Equations Texts.

The American Mathematical Monthly, 1998
(1998). Ordinary Differential Equations Texts. The American Mathematical Monthly: Vol. 105, No. 4, pp. 377-383.
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Invariance for ordinary differential equations

Mathematical Systems Theory, 1967
which remains in S on its maximal interval o f existence. T h e basic theorems in Sections 2 and 3 are the following. 1. I f A C R" is locally compact, g is cont inuous on A and g(x) is subtangential to A at x for every x ~ A N bnd A, then for each x0 ~ A there exists 8 = 8(x0) > 0 and a solution ~b o f (A), 6(0) = x0, which remains in A for 0 ~< t ...
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Optimal Switching for Ordinary Differential Equations

SIAM Journal on Control and Optimization, 1984
The authors consider some deterministic control problems where switching between various controls induces a given cost. Using the known relations between deterministic control problems, dynamic programming arguments, and viscosity solutions of Hamilton-Jacobi equations, the authors study this problem and, in particular, prove the uniqueness of the ...
CAPUZZO DOLCETTA, Italo, L. C. Evans
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