The Study On Phase Shift Properties Based On Symplectic Algorithm

Scholars at home and abroad have scored great successes insymplectic and multi-symplectic methods since Fengkang and Ruthproposed symplectic algorithm for Hamilton systems.One of the most important characteristics of the algorithm ofsymplectic geometry is its structure conservation and long-term trackingability. So its accuracy of the results can be shown in secular computing.The other is its symplectic geometry laws. We may discover newnature laws with the given physical meaning.A coservative system should be symplectic conservative. Hamiltonsystem is a conservative system so symplectic algorithm can be used inthe solutions to the research on mining symplectic laws of Hamiltonsystems.This paper 2～4 chapters were the dissertation research the author hasyielded a series of innovation results in this paper. The theoretical proofof phase shift is proposed aiming at the general type of letters for evevorder linear Hamilton systems with periodic solutions mainly. The phaseshift formulas are given by matching exact solutions and approximatesolutions and using homogeneous deformation for interative matrixaccording to the structive preserving algorithms of symplectic geometry.The essence of phase shift of symplectic algotithm and the correctionshift method are given. Finally a numerical result demonstrate phase shifeof symplectic algorithm. The fifth chapter mainly are defer to"Shanghaijiaotong University math department master the graduatestudent to raise the rule"to complete. After reading and understandingmassive science and technology literature the general report which after the ponder the refinement completes. The fifth chapter which is thegeneral report emphasizes that the application backgrounds of symplecticalgorithm should be considered in small parameter perturbation method,the perturbation of nonlinear systems in ODE, vibration systems andoptimal control systems besides precise symplectic algorithm andsymplectic Runge-Kutta methods. The main idea is to transform thedifferent problems into linear Hamilton systems and solve them withsuitable symplectic difference schemes. Numerical analyses are carriedout to illustrate phase shift of symplectic algorithm in the solution oflinear Hamilton systems.