2025/03/17 by Maximilian Ruff, Ruff, Maximilian · 1 citation
#math.NA #cs.NA #math.AP
paper · pdf · doi:10.1007/s00211-026-01549-z
We study a variant of the Strang splitting for the time integration of the semilinear wave equation under the finite-energy condition on the torus \mathbbT3. In the case of a cubic nonlinearity, we show almost second-order convergence in L2 and almost first-order convergence in H1. If the nonlinearity has a quartic form instead, we show an analogous convergence results, where the order is reduced by 1/2 in both cases. To our knowledge these are the best convergence results available for the 3D cubic and quartic wave equations under the finite-energy condition. Our approach relies on continuous- and discrete-time Strichartz estimates. We also make use of the integration and summation by parts formulas to exploit cancellations in the error terms. Moreover, error bounds for a full discretization using the Fourier pseudo-spectral method in space are given. Finally, we discuss a numerical example indicating the sharpness of our theoretical results.