Symmetric partitioned Runge–Kutta methods for differential equations on Lie groups
نویسندگان
چکیده
منابع مشابه
Lectures on Lie Groups and Differential Equations
The study of symmetry groups and equivalence problems requires a variety of tools and techniques, many of which have their origins in geometry. Even our study of differential equations and variational problems will be fundamentally geometric in nature, in contrast to the analytical methods of importance in existence and uniqueness theory. We therefore begin our exposition with a brief review of...
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The applications of Lie groups to solve differential equations dates back to the original work of Sophus Lie, who invented Lie groups for this purpose. The modern era begins with Birkhoff (1950), and was forged into a key tool of applied mathematics by Ovsiannikov (1982). Basic references are (Hydon, 2000; Olver, 1993, 1995). First we review the geometric approach to systems of differential equ...
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The Exponential Map and Differential Equations on Real Lie Groups
Let G be a connected Lie group with Lie algebra g , expG : g −→ G the exponential map and E(G) its range. E(G) will denote the set of all n -fold products of elements of E(G). G is called exponential if E(G) = E(G) = G . Since most real (or complex) connected Lie groups are not exponential, it is of interest to know that the weaker conclusion E(G) = G is always true (Theorem 5.6). This result w...
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Projection methods are a standard approach for the numerical solution of differential equations on manifolds. It is known that geometric properties (such as symplecticity or reversibility) are usually destroyed by such a discretization, even when the basic method is symplectic or symmetric. In this article, we introduce a new kind of projection methods, which allows us to recover the time-rever...
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ژورنال
عنوان ژورنال: Applied Numerical Mathematics
سال: 2012
ISSN: 0168-9274
DOI: 10.1016/j.apnum.2012.06.029