This analysis reveals error bounds for an implicit-explicit scheme in semilinear wave equations, indicating promising applications in multiscale problems.
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 that 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.
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Eckhardt et al. (2025) studied this question.
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