Two types of second-order in time partial differential equations (PDEs), namely semilinear wave equations and semilinear beam equations are considered. To solve these equations with exponential integrators, we present an approach to compute efficiently the action of the matrix exponential as well as those of related matrix functions. Various numerical simulations are presented that illustrate this approach.

翻译：考虑两种在时间上按时间顺序排列的二阶部分偏差方程,即半线性波方程和半线性光束方程。为了用指数集成器解决这些方程,我们提出了一个方法,以有效计算矩阵指数性动作和相关矩阵函数的动作。提出了各种数字模拟,以说明这一方法。