欧拉-拉格朗日系统的jet辛算法

A Jet Symplectic Algorithm for Euler-Lagrange Systems

研究了在欧拉-拉格朗日系统上的jet辛算法.证明了第二作者在1998年给出的一个离散的欧拉-拉格朗日(DEL)方程存在一个离散形式的几何结构,它沿着解是不变的,这个结构可以通过对离散的作用量函数求导得到.由此,可以给出此格式的jet辛性质.利用这个结构证明了与此DEL方程相关的离散Nother定理.最后,给出了一个欧拉-拉格朗日方程上的jet辛差分格式的数值算例,并与其它的差分格式进行了比较.

A jet symplectic algorithm for Euler-Lagrange systems is studied. It is shown that the discrete Euler-Lagrange（DEL） equation, which was given by the second author in 1998, has fundamental geometric structures that preserve along solutions obtained directly from the variatonal principle. It is shown that these difference schemes are jet symplectic and the Nother＇ s theorem exists by which we give the definition of a discrete version, the momentum map. A numerical example in jet symplectic difference scheme is given. A comparison with other discretization schemes was made.