Numerical study of an analogue of the Boussinesq equation (Q1825613)

Iterative linearization (of \((u^ 2)_{tt})\) and second order finite differences are used to find approximate solutions of \(u_{tt}=u_{xx}+(u^ 2)_{tt}+u_{xxtt}.\) A three level iterative scheme having second order accuracy and a constant coefficient matrix is devised and used in discussing the dynamics of waves having various initial conditions. The computed results are in good agreement with the available exact solitary wave solutions.