シンプレクテック写像の応用について : ハミルトン系の離散版

抄録

Among various applications of symplectic mappings, numerical application is selected. A representation of a symplectic mapping based on a Weinstein generating function is introduced, and it will be shown that the representation is closely related to time-reversibility and leads to such practical schemes as the implicit midpoint method and so on. Moreover, the symmetric Runge-Kutta (abbreviated to RK) method, which has been known as possessing reversibility, is studied from a view point of linear symplecticity. A few dynamical properties intrinsic to linear symplectic RK methods are considered to find that similar properties are inherited by two kinds of RK methods separately when the objects to be integrated are enlarged to nonlinear systems. Finally, two results with respect to numerical reproduction of a phase portrait are dealt with by use of symplectic RK methods.