简谐振子模拟中能量的变化

Change of Energy in the Simulation of Harmonic Oscillators

本文以简谐振子为例讨论在计算机模拟中保守系统的能量变化。模拟和解析分析表明常微分方程通用解法使能量随着时间指数地变化,而Verlet算法只带来振子能量的涨落,能量不会单调变化。这些结果为理解分子动力学模拟算法的特性提供了直观的参考。

Taking the harmonic oscillator as an example,this paper discusses the energy change of conservativesystem in computer simulation. We numerically and analytically show that general methods of solving ordinarydifferential equation make the energy increasing exponentially with time. The Verlet method for molecular dynamicsmake the energy fluctuates rather than monotonically changes. The results are useful for understanding the algorithm ofmolecular simulations.