In this paper, we generalize the exponential energy-preserving integrator proposed in the recent paper [SIAM J. Sci. Comput. 38 (2016) A1876–A1895] for conservative systems, which now becomes linearly implicit by further utilizing the idea of the scalar auxiliary variable approach. Comparing with the original exponential energy-preserving integrator which usually leads to a nonlinear algebraic system, our new method only involves a linear system with a constant coefficient matrix. Taking the nonlinear Klein-Gordon equation and the nonlinear Schrödinger equation for examples, we derive the concrete energy-preserving schemes and demonstrate their high efficiency through numerical experiments.

在本文中，我们对最近提出的[SIAM J. Sci。计算 38（2016）A1876–A1895]，对于保守系统，现在通过进一步利用标量辅助变量方法的思想，线性隐含了。与通常导致非线性代数系统的原始指数能量积分器相比，我们的新方法仅涉及具有常数系数矩阵的线性系统。以非线性Klein-Gordon方程和非线性Schrödinger方程为例，推导了具体的节能方案，并通过数值实验证明了其高效性。