Numerical study of the improved Boussinesq equation

A three-level iterative scheme based on the compact implicit method is devised for solving the improved Boussinesq equation. The scheme has order (h4+h2k2+k2) accuracy and retains the desirable tridiagonal nature of the finite difference equations. A solitary wave solution of the equation is used to examine the accuracy and efficiency of the proposed method. The dynamics of waves having various initial wave packets are discussed.