Computational Methods For Some Non-linear Wave Equations

Some new conservative finite difference schemes are presented for an initial-boundary value problem of the generalized equal width(GEW) equation, the gen-eralized improved KdV(GIKdV) equation and Rosenau-RLW equation. Existence of its difference solutions are proved by Brouwer fixed point theorem. It is proved by the discrete energy method that the schemes are uniquely solvable, unconditionally stable and second-order convergent. Numerical experiments demonstrate that the schemes are accurate efficient.