摘要
In this paper,we present and analyze an energy-conserving and linearly implicit scheme for solving the nonlinear wave equations.Optimal error estimates in time and superconvergent error estimates in space are established without certain time-step restrictions.The key is to estimate directly the solution bounds in the H-norm for both the nonlinear wave equation and the corresponding fully discrete scheme,while the previous investigations rely on the temporal-spatial error splitting approach.Numerical examples are presented to confirm energy-conserving properties,unconditional convergence and optimal error estimates,respectively,of the proposed fully discrete schemes.
基金
supported by National Natural Science Foundation of China (Grant Nos. 11771162,11771128,11871106,11871092 and 11926356)
National Safety Administration Fund (Grant No. U1930402)。