We present an implicit-explicit (IMEX) scheme for semilinear wave equations with strong damping. By treating the nonlinear, nonstiff term explicitly and the linear, stiff part implicitly, we obtain a method which is not only unconditionally stable but also highly efficient. Our main results are error bounds of the full discretization in space and time for the IMEX scheme combined with a general abstract space discretization. As an application, we consider the heterogeneous multiscale method for wave equations with highly oscillating coefficients in space for which we show spatial and temporal convergence rates by using the abstract result.

翻译：本文针对强阻尼半线性波动方程提出了一种隐显式（IMEX）时间离散格式。通过显式处理非线性非刚性项、隐式处理线性刚性项，该方法不仅具有无条件稳定性，同时保持了较高的计算效率。主要研究结果为IMEX格式结合一般抽象空间离散化所构成的全离散格式的误差界。作为应用，我们考察了针对空间高频振荡系数波动方程的异质多尺度方法，并利用前述抽象结果证明了该方法在空间与时间维度上的收敛速率。