The method of iterated commutators for ordinary di erential equations on Lie groups
نویسنده
چکیده
We construct numerical methods to integrate ordinary di erential equations that evolve on Lie groups. These schemes are based on exponentials and iterated commutators, they are explicit and their order analysis is relatively simple. Thus we can construct group-invariant integrators of arbitrarily high order. Among other applications we show that this approach can be used to obtain new symplectic schemes when applied to Hamiltonian problems. Some numerical experiments are presented.
منابع مشابه
Iterated Commutators, Lie's Reduction Method and Ordinary Di erential Equations on Matrix Lie Groups
In the context of devising geometrical integrators that retain qualitative features of the underlying solution, we present a family of numerical methods (the method of iterated commutators, [5, 13]) to integrate ordinary di erential equations that evolve on matrix Lie groups. The schemes apply to the problem of nding a numerical approximation to the solution of Y 0 = A(t;Y )Y; Y (0) = Y0; where...
متن کاملIterated Commutators, Lie's Reduction Method and Ordinary Diierential Equations on Matrix Lie Groups
In the context of devising geometrical integrators that retain qualitative features of the underlying solution, we present a family of numerical methods (the method of iterated commutators, 5, 13]) to integrate ordinary diierential equations that evolve on matrix Lie groups. The schemes apply to the problem of nding a numerical approximation to the solution of Y 0 = A(t;Y)Y; Y (0) = Y0; whereby...
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