A conservative weighted finite difference scheme for regularized long wave equation

In this paper, a new finite difference method for initial-boundary value problem of Regularized Long Wave (RLW) equation is considered. Two energy conservative finite difference schemes are proposed. And the prior estimate of the solution is obtained. Existence and uniqueness of numerical solution are derived. It is proved that the finite difference schemes are convergent and stable. Numerical experiment results show that the theory is accurate and the schemes are efficient and reliable.