Trigonometric time integrators for the Zakharov system
This work provides a provably convergent numerical method for the Zakharov system, addressing a known bottleneck in time integration for PDEs with derivative nonlinearities.
The authors developed a new trigonometric time-integration scheme for the Zakharov system that overcomes the challenge of derivatives in the nonlinearity, achieving a time-step restriction independent of spatial discretization. Numerical experiments confirm the theoretical convergence results.
The main challenge in the analysis of numerical schemes for the Zakharov system originates from the presence of derivatives in the nonlinearity. In this paper a new trigonometric time-integration scheme for the Zakharov system is constructed and convergence is proved. The time-step restriction is independent from a spatial discretization. Numerical experiments confirm the findings.