上海师范大学学报（自然科学版）
上海師範大學學報（自然科學版）
상해사범대학학보（자연과학판）
JOURNAL OF SHANGHAI TEACHERS UNIVERSITY(NATURAL SCIENCES)
2014年
1期
9-21
,共13页
块方法%哈密尔顿系统%线性系统%辛算法%二次型
塊方法%哈密爾頓繫統%線性繫統%辛算法%二次型
괴방법%합밀이돈계통%선성계통%신산법%이차형
block method%linear Hamiltonian system%symplectic integrator%quadratic form
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。
對于哈密爾頓繫統的數值求解，辛算法被認為是最閤適的選擇。主要研究一類具有至少k＋1階收斂性的k維塊方法求解線性哈密爾頓繫統的適用性，證明瞭噹維數k不超過8時該類方法具有保持辛結構和二次型的性質。數值例子驗證瞭理論結果。
대우합밀이돈계통적수치구해，신산법피인위시최합괄적선택。주요연구일류구유지소k＋1계수렴성적k유괴방법구해선성합밀이돈계통적괄용성，증명료당유수k불초과8시해류방법구유보지신결구화이차형적성질。수치례자험증료이론결과。
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.
