SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A2865-A2888, January 2020.
We present linearly implicit methods that preserve discrete approximations to local and global energy conservation laws for multisymplectic partial differential equations with cubic invariants. The methods are tested on the one-dimensional Korteweg--de Vries equation and the two-dimensional Zakharov--Kuznetsov equation; the numerical simulations confirm the conservative properties of the methods and demonstrate their good stability properties and superior running speed when compared to fully implicit schemes.

中文翻译：

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具有三次哈密顿量的偏微分方程的线性隐式局部和全局能量守恒方法

SIAM科学计算杂志，第42卷，第5期，第A2865-A2888页，2020年1月。
我们提出了线性隐式方法，该方法为具有立方不变量的多辛子偏微分方程保留了局部和全局能量守恒定律的离散近似。方法在一维Korteweg-de Vries方程和二维Zakharov-Kuznetsov方程中进行了测试；数值模拟证实了该方法的保守特性，并与全隐式方案相比证明了它们的良好稳定性和优越的运行速度。