4.5 Article

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

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Summary: Two fourth-order compact finite difference schemes, including a Crank-Nicolson scheme and a semi-implicit scheme, are derived for solving the nonlinear Klein-Gordon equations in the nonrelativistic regime. The optimal error estimates, time step selection strategy, and discrete energy conservation are rigorously analyzed. Under proper assumptions, both schemes are proven to have errors of O(h(4)+tau(2)/epsilon(6)), where h is the mesh size and tau is the time step. Numerical simulations confirm the theoretical analysis.

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