共查询到20条相似文献,搜索用时 386 毫秒
1.
WANG Yushun WANG Bin & QIN MengzhaoLASG Institute of Atmospheric Physics Chinese Academy of Sciences Beijing China School of Mathematics Computer Science Nanjing Normal University Nanjing China School of Mathematics System Science Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2004,47(1):18-30
In this paper, taking the 2+1-dimensional sine-Gordon equation as an example, we present the concatenating method to construct the multisymplectic schemes. The-method is to discretizee independently the PDEs in different directions with symplectic schemes, so that the multisymplectic schemes can be constructed by concatenating those symplectic schemes. By this method, we can construct multisymplectic schemes, including some widely used schemes with an accuracy of any order. The numerical simulation on the collisions of solitons are also proposed to illustrate the efficiency of the multisymplectic schemes. 相似文献
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曾文平 《高等学校计算数学学报》2004,26(4):378-384
In this paper, we present two classes of symplectic schemes with high order accuracy for solving four-order rod vibration equation utt uxxxx=0 via the third type generating function method. First, the equation of four order rod vibration is written into the canonical Hamilton system; second, overcoming successfully the essential difficult on the calculus of high order variations derivative, we get the semi-discretization with arbitrary order of accuracy in time direction for the PDEs by the third type generating function method. Furthermore the discretization of the related modified equation of original equation is obtained. Finally, arbitrary order accuracy symplectic schemes are obtained. Numerical results are also presented to show the effectiveness of the scheme, high order accuracy and properties of excellent long-time numerical behavior. 相似文献
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利用连续有限元法得到了二维线性哈密尔顿系统一次元和二次元的计算格式,并证明了它们都是辛格式.系统的内在特征在离散后能保持.本的数值例子也证实了这些结论. 相似文献
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LongGuangHE DeShouZHONG 《数学学报(英文版)》2003,19(4):745-756
In this paper,some properties of reduction for symplectic F-spaces are discussed.The properties of stable subgroups are discussed.We find that the symplectic action of a symplectic groupoid on a symplectic manifold can induce a symplectic map between reduced symplectic manifolds.This symplectic action can be characterized by the action of its induced symplectic groupoid on a symplectic manifold.Lastly,we shall discuss Poisson reduction and give a Poisson reduction theorem. 相似文献
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In this paper, similarity symplectic geometry for curves is proposed and studied. Explicit expressions of the symplectic invariants, Frenet frame and Frenet formulae for curves in similarity symplectic geometry are obtained by using the equivariant moving frame method. The relationships between the Euclidean symplectic invariants, Frenet frame, Frenet formulae and the similarity symplectic invariants, Frenet frame, Frenet formulae for curves are established. Invariant curve flows in four-dimensional similarity symplectic geometry are also studied. It is shown that certain intrinsic invariant curve flows in four-dimensional similarity symplectic geometry are related to the integrable Burgers and matrix Burgers equations. 相似文献
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Hong-yuLiu GengSun 《计算数学(英文版)》2004,22(5):769-776
Properties of symplectic Runge-Kutta (RK) methods and symplectic partitioned Runge-Kutta (PRK) methods with real eigenvalues are discussed in this paper. It is shown that an s stage such method can‘t reach order more than s 1. Particularly, we prove that no symplectic RK method with real eigenvalues exists in stage s of order s 1 when s is even. But an example constructed by using the W-transformation shows that PRK method of this type does not necessarily meet this order barrier. Another useful way other than W-transformation to construct symplectic PRK method with real eigenvalues is then presented. Finally, a class of efficient symplectic methods is recommended. 相似文献
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The connection between closed Newton–Cotes, trigonometrically-fitted differential methods and symplectic integrators is studied in this paper. Several one-step symplectic integrators have been obtained based on symplectic geometry, as is shown in the literature. However, the study of multi-step symplectic integrators is very limited. The well-known open Newton–Cotes differential methods are presented as multilayer symplectic integrators by Zhu et al. [W. Zhu, X. Zhao, Y. Tang, Journal of Chem. Phys. 104 (1996), 2275]. The construction of multi-step symplectic integrators based on the open Newton–Cotes integration methods is investigated by Chiou and Wu [J.C. Chiou, S.D. Wu, Journal of Chemical Physics 107 (1997), 6894]. The closed Newton–Cotes formulae are studied in this paper and presented as symplectic multilayer structures. We also develop trigonometrically-fitted symplectic methods which are based on the closed Newton–Cotes formulae. We apply the symplectic schemes in order to solve Hamilton’s equations of motion which are linear in position and momentum. We observe that the Hamiltonian energy of the system remains almost constant as the integration proceeds. Finally we apply the new developed methods to an orbital problem in order to show the efficiency of this new methodology. 相似文献
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In this paper we discuss relations between symplectic forms and smooth structures on closed manifolds. Our main motivation is the problem if there exist symplectic structures on exotic tori. This is a symplectic generalization of a problem posed by Benson and Gordon. We give a short proof of the (known) positive answer to the original question of Benson and Gordon that there are no Kähler structures on exotic tori. We survey also other related results which give an evidence for the conjecture that there are no symplectic structures on exotic tori. 相似文献
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Ion Alexandru Mihai 《Transformation Groups》2007,12(3):573-599
We define the odd symplectic Grassmannians and flag manifolds, which are smooth projective varieties equipped with an action
of the odd symplectic group, analogous to the usual symplectic Grassmannians and flag manifolds. Contrary to the latter, which
are the flag manifolds of the symplectic group, the varieties we introduce are not homogeneous. We argue nevertheless that
in many respects the odd symplectic Grassmannians and flag manifolds behave like homogeneous varieties; in support of this
claim, we compute the automorphism group of the odd symplectic Grassmannians and we prove a Borel-Weil-type theorem for the
odd symplectic group. 相似文献
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In this paper we study the persistence of lower dimensional hyperbolic invariant tori for nearly integrable twist symplectic mappings. Under a Rüssmann-type non-degenerate condition, by introducing a modified KAM iteration scheme, we proved that nearly integrable twist symplectic mappings admit a family of lower dimensional hyperbolic invariant tori as long as the symplectic perturbation is small enough. 相似文献
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s级p阶辛Runge-Kutta-Nystr\"om(R-K-N)方法的一种充要条件是用关于参数的非线性方程组来表示的,辛R-K-N格式的构造问题因而转化为该方程组的求解问题. 在一些特殊的限定条件下, 已有该方程组在s=3,p=4时的两组解,即得到了两个三级四阶显式辛格式. 对于s=3,p=4情形,基于吴方法,利用计算机代数系统Maple及软件包wsolve给出了对应的非线性方程组的全部解, 这样就构造了所有的三级四阶显式辛R-K-N格式, 并证明了三级四阶显式辛R-K-N方法所满足的条件方程有冗余. 数值实验结果显示出新的辛格式在一定的条件下有着较好的误差精度. 相似文献
13.
Ma Renyi 《数学学报(英文版)》1996,12(4):379-384
In this note, we prove that the symplectic blow-up or blow-down in the dimension 4 is rigid, i.e. the symplectic area of the divisor does not exceed the symplectic radius of the neighbourhood on which we do the blow-up or blow-down.Supported in part by the NSF of P. R. China and the Foundation of Chinese Educational Committee for Returned Scholars. 相似文献
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In this paper, we systematically construct two classes of structure-preserving schemes with arbitrary order of accuracy for canonical Hamiltonian systems. The one class is the symplectic scheme, which contains two new families of parameterized symplectic schemes that are derived by basing on the generating function method and the symmetric composition method, respectively. Each member in these schemes is symplectic for any fixed parameter. A more general form of generating functions is introduced, which generalizes the three classical generating functions that are widely used to construct symplectic algorithms. The 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 step. The existence of the solutions of these schemes is verified. Numerical experiments demonstrate the theoretical analysis and conservation of the proposed schemes. 相似文献
15.
We derive a criterion that any general linear method must satisfy if it is symplectic. It is shown, by considering the method
over several steps, that the satisfaction of this condition leads to a reducibility in the method. Linking the symplectic
criterion here to that for Runge–Kutta methods, we demonstrate that a general linear method is symplectic only if it can be
reduced to a method with a single input value.
相似文献
16.
Susan Tolman 《Inventiones Mathematicae》1998,131(2):299-310
An important question with a rich history is the extent to which the symplectic category is larger than the K?hler category.
Many interesting examples of non-K?hler symplectic manifolds have been constructed [T] [M] [G]. However, sufficiently large
symmetries can force a symplectic manifolds to be K?hler [D] [Kn]. In this paper, we solve several outstanding problems by
constructing the first symplectic manifold with large non-trivial symmetries which does not admit an invariant K?hler structure.
The proof that it is not K?hler is based on the Atiyah-Guillemin-Sternberg convexity theorem [At] [GS]. Using the ideas of
this paper, C. Woodward shows that even the symplectic analogue of spherical varieties need not be K?hler [W].
Oblatum IX-1995 & 3-III-1997 相似文献
17.
Yildiray Ozan 《Proceedings of the American Mathematical Society》2005,133(4):1223-1230
In this work we define a relative version of the flux homomorphism, introduced by Calabi in 1969, for a symplectic manifold. We use it to study (the universal cover of) the group of symplectomorphisms of a symplectic manifold leaving a Lagrangian submanifold invariant. We also show that some quotients of the universal covering of the group of symplectomorphisms are stable under symplectic reduction.
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L. Brugnano 《计算数学(英文版)》1997,15(3):233-252
1.IlltroductiollInmanyareasofphysics,mechanics,etc.,HamiltoniansystemsofODEsplayaveryimportantrole.Suchsystemshavethefollowinggeneralform:where,bydenotingwithOfandimthenullmatrixandtheidentitymatrixofordermarespectively,SimplepropertiesofthematrixJZmarethefollowingones:Inequation(1)AH(~,t)isthegradientofascalarfunctionH(y,t),usuallycalledHamiltonian.InthecasewhereH(y,t)=H(y),thenthevalueofthisfunctionremainsconstantalongt.hesollltion7/(t),t,hatis'*ReceivedFebruaryI3,1995.l)Worksupporte… 相似文献
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Roberto Paoletti 《Israel Journal of Mathematics》2001,123(1):241-251
By working on the symplectic blow-up, we show that the symplectic divisors produced by Donaldson in [D] may be chosen so that
they contain a fixed symplectic submanifold or, in a complementary direction, so that they cut it transversally with a symplectic
intersection. 相似文献