منابع مشابه
Commutator-free Lie group methods
RKMK methods and Crouch-Grossman methods are two classes of Lie group methods. The former is using flows and commutators of a Lie algebra of vector fields as a part of the method definition. The latter uses only compositions of flows of such vector fields, but the number of flows which needs to be computed is much higher than in the RKMK methods. We present a new type of methods which avoids th...
متن کاملOrder conditions for commutator-free Lie group methods
We derive order conditions for commutator-free Lie group integrators. These schemes can for certain problems be good alternatives to the Runge-Kutta-Munthe-Kaas schemes, especially when applied to stiff problems or to homogeneous manifolds with large isotropy groups. The order conditions correspond to a certain subsets of the set of ordered rooted trees. We discuss ways to select these subsets ...
متن کاملLie Group Methods *
Definition 1.1. [Ol] An m-dimensional manifold M is a topological space covered by a collection of open subsets Wα ⊂M (coordinate charts) and maps Xα : Wα → Vα ⊂ R one-to-one and onto, where Vα is an open, connected subset of R. (Wα,Xα) define coordinates on M. M is a smooth manifold if the maps Xαβ = Xβ ◦X−1 α , are smooth where they are defined, i.e. on Xα(Wα ∩Wβ) to Xβ(Wα ∩Wβ). Example 1.2. ...
متن کاملThe Higher Commutator Subgroups of a Group
It is not the object of this address to introduce you to new theories or to tell of great discoveries. Quite on the contrary; I intend to speak of unsolved problems and of conjectures. In order to describe these, certain concepts will have to be discussed ; and for obtaining a proper perspective it will be necessary to mention a number of theorems, some of them new. The proofs of the latter wil...
متن کاملCommutator width in the first Grigorchuk group
Let G be the first Grigorchuk group. We show that the commutator width of G is 2: every element g ∈ [G, G] is a product of two commutators, and also of six conjugates of a. Furthermore, we show that every finitely generated subgroup H ≤ G has finite commutator width, which however can be arbitrarily large, and that G contains a subgroup of infinite commutator width. The proofs were assisted by ...
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ژورنال
عنوان ژورنال: Future Generation Computer Systems
سال: 2003
ISSN: 0167-739X
DOI: 10.1016/s0167-739x(02)00161-9