We consider a kind of differential equations d/dt y(t) = R(y(t))y(t) + f(y(t)) with energy conservation. Such conservative models appear for instance in quantum physics, engineering and molecular dynamics. A new class of energy-preserving schemes is constructed by the ideas of scalar auxiliary variable (SAV) and splitting, from which the nonlinearly implicit schemes have been improved to be linearly implicit. The energy conservation and error estimates are rigorously derived. Based on these results, it is shown that the new proposed schemes have unconditionally energy stability and can be implemented with a cost of solving a linearly implicit system. Numerical experiments are done to confirm these good features of the new schemes.

翻译：我们考虑一类具有能量守恒性质的微分方程 d/dt y(t) = R(y(t))y(t) + f(y(t))。这类保守模型出现在量子物理、工程学和分子动力学等领域。通过引入标量辅助变量(SAV)和分裂方法的思想，构造了一类新的保能量格式，将原有的非线性隐式格式改进为线性隐式格式。严格推导了能量守恒性和误差估计。基于这些结果，表明新提出的格式具有无条件能量稳定性，并且可以以求解线性隐式系统的计算成本实现。数值实验验证了新格式的这些优良特性。