Research on the discrete variational method for a Birkhoffian system
Research on the discrete variational method for a Birkhoffian system
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DOI：
10.1088/1674-1056/23/6/064501
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发表时间：
2014-04
影响因子：
1.7
通讯作者：
Shixing Liu;Wei Hua;Yongxin Guo
中科院分区：
文献类型：
--
作者：
Shixing Liu;Wei Hua;Yongxin Guo
本文基于离散Pfaff-Birkhoff原理，提出了一种新的Birkhoff系统积分算法。证明了新算法能保持Birkhoff系统的一般辛几何结构。对阻尼振子系统进行了数值实验。结果表明，新算法比R-K方法能更好地模拟能量耗散，说明对于具有一般辛结构的系统，可以在Birkhoff框架下用离散变分方法数值求解动力学方程.进一步证明了数值实验的结果并不取决于Birkhoff函数的构造方法，而是取决于数值方法能否保持动力系统的固有性质.
In this paper, we present a new integration algorithm based on the discrete Pfaff—Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structures of Birkhoffian systems. A numerical experiment for a damping oscillator system is conducted. The result shows that the new algorithm can better simulate the energy dissipation than the R-K method, which illustrates that we can numerically solve the dynamical equations by the discrete variational method in a Birkhoffian framework for the systems with a general symplectic structure. Furthermore, it is demonstrated that the results of the numerical experiments are determined not by the constructing methods of Birkhoffian functions but by whether the numerical method can preserve the inherent nature of the dynamical system.