Efficient local structure-preserving schemes for the RLW-type equation

The multisymplectic schemes have been used in numerical simulations for the RLW-type equation successfully. They well preserve the local geometric property, but not other local conservation laws. In this article, we propose three novel efficient local structure-preserving schemes for the RLW-type equation, which preserve the local energy exactly on any time-space region and can produce richer information of the original problem. The schemes will be mass- and energy-preserving as the equation is imposed on appropriate boundary conditions. Numerical experiments are presented to verify the efficiency and invariant-preserving property of the schemes. Comparisons with the existing nonconservative schemes are made to show the behavior of the energy affects the behavior of the solution.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2017