构造哈密尔顿系统jet辛差分格式的生成函数法

The Construction of Jet Symplectic Difference Scheme for Hamiltonian Systems via Generating Functions

考虑哈密尔顿系统的保结构算法,在经典哈密尔顿系统的jet辛算法的基础上,给出了一般哈密尔顿系统的jet辛差分格式的定义.并利用带有变系数辛矩阵的一般哈密尔顿系统中的构造辛差分格式的生成函数法的思想,来建立由一般的反对称矩阵所确定的微分二形式与生成函数的关系,再利用哈密尔顿-雅可比方程来构造jet辛的差分格式.

A method preserving structures of the Hamiltonian systems is considered. On the basis of the jet symplectic difference scheme for canonical Hamiltonians the jet symplectic difference scheme for Hamiltonian systems in general symplectic structure with variable coefficientsic is defined . According to the general approach of the generating function method for the symplectic difference schemes a relation between the general symplectic structure and the generating functions is found. The jet symplectic difference schemes for classical Hamiltonian systems are constructed in terms of Hamilton-Jacobi equation.