摘要
与Runge-Kutta(RK)方法相比,辛算法具有保持相空间辛结构不变或保哈密顿函数不变的突出优点。但是,在时域上,同阶的辛算法与Runge-Kutta法具有相同的数值精度,即辛算法在计算过程中也存在相位误差,导致解的数值精度不高。为了提高辛算法在时域上解的精度,首先根据哈密顿函数的特点将哈密顿系统归结为2种类型,然后建立了不同类型下辛算法的相位误差公式,归纳出各类相位漂移的特点,进而提出了一种适当的纠漂方法,使得辛算法在时域上获得了很高的数值精度。相关算例的数值结果验证了纠漂理论的有效性和可靠性。
In the phase space, the symplectic algorithm has the outstanding advantages of conserving the symplectic structure and laws of the Hamiltonian system, compared with Runge-Kutta （RK） method. But in the time domain, because of phase-lags, they have the same algebraic order precision under the condition of the same algebraic order of schemes. In order to improve the precision of numeri- cal solutions in the time domain, two kinds of phase-lag formulas of symplectic algorithm are built by the different types of Hamiltonian system based on the character of Hamiltonian functions. According to the characters of different phase-lag, the techniques of rectifying drifts are proposed. So the precision of numerical solution computed by symplectic method are improved. The results of numerical examples demonstrate the reliability and effectiveness of the phase-lag formula and drifting techniques.
出处
《上海第二工业大学学报》
2015年第4期325-330,共6页
Journal of Shanghai Polytechnic University
基金
上海第二工业大学校基金项目(No.EGD15XQD14)
上海第二工业大学重点学科项目(No.XXKZD1304)资助
上海高校青年教师培养资助计划(No.ZZZZEGD15007)
