Uniform error bound of a conservative fourth-order compact finite difference scheme for the Zakharov system in the subsonic regime

In this paper, we use the order reduction method to present a Crank–Nicolson‐type finite difference scheme for Zakharov system (ZS) with a dimensionless parameter ε∈false(0,1false]$$ \varepsilon \in \left(0,1\right] $$, which is inversely proportional to the ion acoustic speed. The proposed scheme is proved to perfectly inherit the mass and energy conservation possessed by ZS, while the invariants satisfied by most existing schemes are expressed by two‐level's solution at each time step. In the subsonic limit regime, that is, when 0<ε≪1$$ 0<\varepsilon \ll 1 $$, the solution of ZS propagates rapidly oscillatory initial layers in time, and this brings significant difficulties in designing numerical methods and establishing the error estimates, especially in the subsonic limit regime. After proving the solvability of the proposed scheme, we use the cut‐off function technique and energy method to rigorously analyze two independent error estimates for the well‐prepared, less‐ill‐prepared, ill‐prepared initial data, respectively, which are uniform in both time and space for ε∈false(0,1false]$$ \varepsilon \in \left(0,1\right] $$ and optimal at second order in space. Numerical examples are carried out to verify the theoretical results and show the effectiveness of the proposed scheme.

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“…In [27], they further proposed a time splitting combined with exponential wave integrator sine pseudospectral method for the classical ZS with

\varepsilon \in \left(0,1\right]

. Recently, Zhang and Wang [28] proposed a fourth‐order compact finite difference scheme for ZS ()–() and established the uniform error estimate.…”

Section: Introductionmentioning

confidence: 99%

Uniform error bound of a Crank–Nicolson‐type finite difference scheme for Zakharov system in the subsonic limit regime

Wang

Yang

2023

Math Methods in App Sciences

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A new high-accuracy difference method for nonhomogeneous time-fractional Schrödinger equation

Tian

Cao

Yang

2023

International Journal of Computer Mathematics

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Uniform error bound of a conservative fourth-order compact finite difference scheme for the Zakharov system in the subsonic regime

Cited by 2 publications

References 28 publications

Uniform error bound of a Crank–Nicolson‐type finite difference scheme for Zakharov system in the subsonic limit regime

Uniform error bound of a Crank–Nicolson‐type finite difference scheme for Zakharov system in the subsonic limit regime

A new high-accuracy difference method for nonhomogeneous time-fractional Schrödinger equation

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