基于修正的Magnus方法的高振荡动力系统的数值积分方法

基于建立于一般线性动力系统上的Magnus数值积分方法,针对随时间而高频率振荡的二阶动力系统,给出了有效的修正Magnus数值积分算法．首先,将二阶动力系统重新表示为一阶系统的形式,通过引进新变量进行参考坐标变换，使动力系统的高振荡性质保留在新形式内;进而基于局部线性化技术用修正的Magnus方法求解新形式下的系统方程;最后,通过一系列数值实验说明了文中方法的有效性．

Efficient Numerical Integrators for Highly Oscillatory Dynamic Systems Based on Modified Magnus Integrator Method

Based on the Magnus integrator method established in linear dynamic systems, an efficiently improved modified Magnus integrator method is proposed for the second-order dynamic systems with time-dependent high frequencies. Firstly, the second-order dynamic system was reformulated as a system of the first-order and transfered the frame of reference by introducing new variables so that highly oscillatory behaviour is inherited from the entries in the meantime. Then the modified Magnus integrator method based on local linearization was appropriately-designed for solving the above new form and some improved ones are also presented. Finally, numerical examples are presented and analyzed to show that the proposed methods appear to be quite adequate for integration for highly oscillatory dynamic systems including Hamiltonian systems problem with long time and effectiveness.