Unconditionally optimal convergence of an energy-conserving and linearly implicit scheme for nonlinear wave equations

In this paper, we present and analyze an energy-conserving linearly implicit scheme for solving the nonlinear wave equations. Optimal error estimates in time superconvergent space are established without certain time-step restrictions. The key is to estimate directly solution bounds H2-norm both equation corresponding fully discrete scheme, while previous investigations rely on temporal-spatial splitting approach. Numerical examples presented confirm properties, unconditional convergence optimal estimates, respectively, of proposed schemes.