Exponential integrators based on discrete gradient methods are applied to non-canonical Hamiltonian systems with added linear forcing/damping terms, which may be time-dependent. Changes in the dynamics, such as conservation of energy or Casimirs, which result from inclusion of the linear forcing/damping terms, are not exactly preserved by standard discrete gradient methods. However, those changes are shown to be exactly preserved by the exponential integrators in special circumstances. The methods are also symmetric, second order, and linearly stable. To demonstrate advantages in both accuracy and efficiency over other standard methods, the exponential integrators are applied to a three dimensional Lotka-Volterra system and a damped/driven Ablowitz-Ladik system.

将基于离散梯度方法的指数积分器应用于具有时间依赖性的线性强迫/阻尼项的非规范哈密顿系统。标准离散梯度方法不能完全保留由线性强迫/阻尼项引起的动力学变化，例如能量守恒或卡西米尔的守恒。但是，在特殊情况下，这些变化被指数积分器精确地保留了下来。这些方法也是对称的，二阶的和线性稳定的。为了证明在精度和效率上均优于其他标准方法，指数积分器应用于三维Lotka-Volterra系统和阻尼/驱动Ablowitz-Ladik系统。