摘要
辛算法和保能量算法是应用最为广泛的两种保结构算法.本文从相位误差的角度给出了他们的比较结果.我们针对线性动力系统,分别分析了基于Pade对角逼近给出的辛算法和基于平均向量场法得到的能量守恒算法的相位误差,并通过数值验证了分析结果.文章还给出了保结构算法相位误差的改进方法,并通过数值例子验证了方法的有效性.
Symplectic and energy preserving methods are two most widely used structure-preserving algorithms. In this paper, we present a comparison of theses methods from the point of phase errors. For the linear dynamic system, we give the numerical analysis of the phase errors for the energy preserving methods based on the diagonal Páde approximation and the average vector field method, respectively. Numerical experiments verifies our theoretical resault. We also propose a method for the improvement of the phase error whose validity is confirmed by the numerical tests.
出处
《计算数学》
CSCD
北大核心
2014年第3期271-290,共20页
Mathematica Numerica Sinica
基金
国家自然科学基金(11271195
41231173)
江苏省气候变化协同创新中心资助
关键词
辛方法
对角Páde逼近
平均向量场法
相位误差
相位修正
symplectic method
diagonal Páde approximation
average vector fieldmethod
phase error
phase correction
