We present a new linearly implicit exponential integrator that preserves the polynomial first integrals or Lyapunov functions for the conservative and dissipative stiff equations, respectively. The method is tested by both oscillated ordinary differential equations and partial differential equations, e.g., an averaged system in wind-induced oscillation, the Fermi-Pasta-Ulam systems, and the polynomial pendulum oscillators. The numerical simulations confirm the conservative properties of the proposed method and demonstrate its good behavior in superior running speed when compared with fully implicit schemes for long-time simulations.

翻译：我们提出了一个新的线性隐含指数集成器,为保守的和消散的硬方程式分别保留了多边第一组合体或Lyapunov函数。该方法由振动的普通差分方程式和部分差分方程式测试,例如,风引发振荡的平均系统、Fermi-Pasta-Ulam系统,以及多元钟振荡器。数字模拟证实了拟议方法的稳妥性,并表明与长期模拟完全隐含的计划相比,其运行速度较快,表现良好。