Zubov's method is a technique for computing the basin of attraction for a set of ordinary differential equations (a dynamical system). The domain of attraction is the set, where is the solution to a partial differential equation known as the Zubov equation. 'Zubov's method' can be used in a number of ways.
Zubov's theorem states that:
- If is an ordinary differential equation in with, a set containing 0 in its interior is the domain of attraction of zero if and only if there exist continuous functions such that:
- , for, on
- for every there exist such that, if
- for or
If f is continuously differentiable, then the differential equation has at most one continuously differentiable solution satisfying .
Famous quotes containing the word method:
“Argument is conclusive ... but ... it does not remove doubt, so that the mind may rest in the sure knowledge of the truth, unless it finds it by the method of experiment.... For if any man who never saw fire proved by satisfactory arguments that fire burns ... his hearer’s mind would never be satisfied, nor would he avoid the fire until he put his hand in it ... that he might learn by experiment what argument taught.”
—Roger Bacon (c. 1214–1294)