线性哈密尔顿系统的块方法(英文)

Block methods for linear Hamiltonian systems

对于哈密尔顿系统的数值求解,辛算法被认为是最合适的选择.主要研究一类具有至少k+1阶收敛性的k维块方法求解线性哈密尔顿系统的适用性,证明了当维数k不超过8时该类方法具有保持辛结构和二次型的性质.数值例子验证了理论结果.

For the numerical treatment of Hamiltonian differential equations,symplectic integrators are regarded as the most suitable choice.In this paper we are concerned with the applicability of block methods for the discrete approximate solution of linear Hamiltonian systems.The k-dimensional block methods are convergent of order at least k＋1 for ordinary differential equations.We provide conditions on the coefficients of the equivalent block methods in order to maintain two important properties of linear Hamiltonian problems.It is shown that the k-dimensional block method which is convergent of order at least k＋1 is symplectic and preserves the quadratic form at the last point of the block for k=1 ,2,…,8.Numerical experiment is given to illustrate the performance of the block methods.