Structure-preserving finite difference schemes for nonlinear wave equations with dynamic boundary conditions

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.