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.(c) 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1678-1691, 2017