Energy stable schemes for the Klein-Gordon-Zakharov equations

Based on the traditional scalar auxiliary variable (SAV) method, the exponential SAV (ESAV) method, and the Lagrange multiplier method, three efficient energy stable schemes are proposed to solve the Klein-GordonZakharov equations. All proposed schemes lead to linear equations with constant coefficients to be solved in each time step. The first two schemes are proved to preserve two different modified energies respectively and both of them can be solved efficiently. The third one can maintain the original energy conservation property, but it requires solving an additional nonlinear algebraic equation. Several numerical examples are given to verify the accuracy, efficiency, and energy stability of the three schemes.

Automated summary

Three efficient energy stable schemes are proposed to solve the Klein-Gordon-Zakharov equations, based on the traditional scalar auxiliary variable (SAV) method, the exponential SAV (ESAV) method, and the Lagrange multiplier method. These schemes lead to linear equations with constant coefficients to be solved in each time step, preserving modified energies or original energy conservation property. Numerical examples are provided to verify the accuracy, efficiency, and energy stability of the schemes.