  In this article we discuss the numerical analysis for the finite difference
scheme of the one-dimensional nonlinear wave equations with dynamic boundary
conditions. From the viewpoint of the discrete variational derivative method we
propose the derivation of the structure-preserving finite difference schemes of
the problem which covers a variety of equations as widely as possible. Next, we
focus our attention on the semilinear wave equation, and show the existence and
uniqueness of solution for the scheme and error estimates with the help of the
inherited energy structure.
