A new multi-symplectic Euler box scheme for the BBM equation

A new scheme for the BBM equation with the accuracy order of O(△t2+△x2) is proposed. The multi-symplectic conservation property of the new scheme is proved. The backward error analysis of the new scheme is implemented. The solitary wave evolution behaviors are simulated by the new scheme. The new multi-symplectic Euler box scheme is compared with the classical Euler box scheme and the Preissman box scheme in preserving the conservation properties of the BBM equation and the computation cost.