A fourth-order compact finite difference scheme for the quantum Zakharov system that perfectly inherits both mass and energy conservation

In this paper, we propose and analyze a new fourth-order compact finite difference scheme for solving the quantum Zakharov system (QZS). The new scheme perfectly inherits the mass and energy conservation possessed by the QZS, while the energy preserved by the existing schemes expressed by two-level's solution at each time step. By using the energy method to analyze an equivalent form of the difference scheme, without any requirement on the grid ratio, we establish rigorously the optimal error estimate of the proposed scheme in the energy norm. The accuracy is shown to be fourth order in space and second order in time. Numerical examples are presented to verify the theoretical results and show the effectiveness of the proposed scheme. (c) 2022 IMACS. Published by Elsevier B.V. All rights reserved.

Automated summary

In this paper, a new fourth-order compact finite difference scheme is proposed for solving the quantum Zakharov system. The scheme preserves the mass and energy conservation properties of the system, while also preserving the energy at each time step. By analyzing the equivalent form of the difference scheme using the energy method, rigorous optimal error estimates are established in the energy norm. The scheme demonstrates fourth-order accuracy in space and second-order accuracy in time. Numerical examples validate the theoretical results and demonstrate the effectiveness of the proposed scheme.