A numerical method for the Hamiltonian system is required to preserve some structure-preserving properties. The current structure-preserving method satisfies the requirements that a symplectic method can preserve the symplectic structure of a finite dimension Hamiltonian system, and a multi-symplectic method can preserve the multi-symplectic structure of an infinite dimension Hamiltonian system. In this paper,the structure-preserving properties of three differential schemes for an oscillator system are investigated in detail. Both the theoretical results and the numerical results show that the results obtained by the standard forward Euler scheme lost all the three geometric properties of the oscillator system, i.e., periodicity, boundedness, and total energy,the symplectic scheme can preserve the first two geometric properties of the oscillator system, and the St¨ormer-Verlet scheme can preserve the three geometric properties of the oscillator system well. In addition, the relative errors for the Hamiltonian function of the symplectic scheme increase with the increase in the step length, suggesting that the symplectic scheme possesses good structure-preserving properties only if the step length is small enough. 相似文献
With the help of the coordinate transformation technique, the symplectic dual solving system is developed for multi-material wedges under antiplane deformation. A virtue of present method is that the compatibility conditions at interfaces of a multi-material wedge are expressed directly by the dual variables, therefore the governing equation of eigenvalue can be derived easily even with the increase of the material number. Then, stress singularity on multi-material wedges under antiplane deformation is investigated, and some solutions can be presented to show the validity of the method. Simultaneously, an interesting phenomenon is found and proved strictly that one of the singularities of a special five-material wedge is independent of the crack direction. 相似文献
Estimation of the error arising in the cost (goal) functional due to stopping the iterative process is considered for a steady problem solved by temporal relaxation. The functional error is calculated using an iteration residual along with related adjoint parameters. Numerical tests demonstrate the applicability of this approach for the steady 2D Euler equations. 相似文献
Linear and nonlinear Hamiltonian systems are studied on time scales
. We unify symplectic flow properties of discrete and continuous Hamiltonian systems. A chain rule which unifies discrete and continuous settings is presented for our so-called alpha derivatives on generalized time scales. This chain rule allows transformation of linear Hamiltonian systems on time scales under simultaneous change of independent and dependent variables, thus extending the change of dependent variables recently obtained by Do
lý and Hilscher. We also give the Legendre transformation for nonlinear Euler–Lagrange equations on time scales to Hamiltonian systems on time scales. 相似文献
Localized and non-localized acoustic receptivity for a Blasius boundary layer is investigated using the adjoint Parabolized
Stability Equations. The scattering of an acoustic wave onto a hump, a rectangular roughness or a wall steady blowing and
suction is described. Comparisons with local approaches, triple deck theory, direct numerical simulations and experiments
are successfully shown. Non-parallel effects are discussed. For comparable parameters, the non-localized receptivity problem
produces amplitudes one order of magnitude larger than for the case of localized receptivity.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
l introductionThe vortex system is a system of POint voids, and a model Of incompressible inviscidnow inspired by the idea of an almOSt POtence flOW. The voracity in the now is concentratedin N-vortices (i. e., POints at which the vortloty field is singUlar) [4]. An ideal incompressible now can be approximated by the motion Of a ~ system which is not only a usefulheuristic tool in the analysis of the general propelles of solutionS Of Euler equations, but also auseful stachg POint for th… 相似文献
The three-body problem with all the classical integrals fixed and all the symmetries removed is called the reduced three-body problem. We use the methods of symplectic scaling and reduction to show that the reduced planar or spatial three-body problem with one small mass is to the first approximation the product of the restricted three-body problem and a harmonic oscillator. This allows us to prove that many of the known results for the restricted problem have generalizations for the reduced three-body problem.
For example, all the non-degenerate periodic solutions, generic bifurcations, Hamiltonian-Hopf bifurcations, bridges and natural centers known to exist in the restricted problem can be continued into the reduced three-body problem. The classic normalization calculations of Deprit and Deprit-Bartholomé show that there are two-dimensional KAM invariant tori near the Lagrange point in the restricted problem. With the above result this proves that there are three-dimensional KAM invariant tori near the Lagrange point in the reduced three-body problem. 相似文献