Trigonometric time integrators for the Zakharov system

TL;DR

This paper introduces a new trigonometric time-integration scheme for the Zakharov system, proving its convergence and demonstrating its effectiveness through numerical experiments, with a time-step restriction independent of spatial discretization.

Contribution

A novel trigonometric time-integration scheme for the Zakharov system is developed and its convergence is rigorously proven, addressing derivative nonlinearities.

Findings

Convergence of the proposed scheme is established.

Numerical experiments confirm the theoretical results.

Time-step restriction is independent of spatial discretization.

Abstract

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.