In this paper,we systematically construct two classes of structure-preserving schemes with arbitrary order of accuracy for canonical Hamiltonian *** one class is the symplectic scheme,which contains two new families o...
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In this paper,we systematically construct two classes of structure-preserving schemes with arbitrary order of accuracy for canonical Hamiltonian *** one class is the symplectic scheme,which contains two new families of parameterized symplectic schemes that are derived by basing on the generatingfunction method and the symmetric composition method,*** member in these schemes is symplectic for any fixed parameter.A more general form of generatingfunctions is introduced,which generalizes the three classical generatingfunctions that are widely used to construct symplectic *** other class is a novel family of energy and quadratic invariants preserving schemes,which is devised by adjusting the parameter in parameterized symplectic schemes to guarantee energy conservation at each time *** existence of the solutions of these schemes is *** experiments demonstrate the theoretical analysis and conservation of the proposed schemes.
Non-canonical Hamiltonian systems have K-symplectic structures which are preserved by K-symplectic numerical integrators. There is no universal method to construct K-symplectic integrators for arbitrary non-canonical ...
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Non-canonical Hamiltonian systems have K-symplectic structures which are preserved by K-symplectic numerical integrators. There is no universal method to construct K-symplectic integrators for arbitrary non-canonical Hamiltonian systems. However, in many cases of interest, by using splitting, we can construct explicit K-symplectic methods for separable non-canonical systems. In this paper, we identify situations where splitting K-symplectic methods can be constructed. Comparative numerical experiments in three non-canonical Hamiltonian problems show that symmetric/non-symmetric splitting K-symplectic methods applied to the non-canonical systems are more efficient than the same-order Gauss' methods/non-symmetric symplectic methods applied to the corresponding canonicalized systems;for the non-canonical Lotka-Volterra model, the splitting algorithms behave better in efficiency and energy conservation than the K-symplectic method we construct via generatingfunction technique. In our numerical experiments, the favorable energy conservation property of the splitting K-symplectic methods is apparent. (C) 2016 Elsevier Inc. All rights reserved.
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