منابع مشابه
Lie 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. ...
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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...
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For the eigenvalue function on symmetric matrices, we have gathered a number of it’s properties.We show that this map has the properties of continuity, strict continuity, directional differentiability, Frechet differentiability, continuous differentiability. Eigenvalue function will be extended to a larger set of matrices and then the listed properties will prove again.
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In this paper we present a technique for reducing to a minimum the number of commutators required in the practical implementation of Lie group methods for integrating numerically matrix differential equations. This technique is subsequently applied to the linear and nonlinear case for constructing new geometric integrators, optimal with respect to the number of commutators. © 2002 Elsevier Scie...
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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 ...
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ژورنال
عنوان ژورنال: Journal of Generalized Lie Theory and Applications
سال: 2016
ISSN: 1736-4337
DOI: 10.4172/1736-4337.1000240