A Splitting Method for the Benjamin-Bona-Mahoney Equation Using WENO Scheme

Abstract

The Benjamin-Bona-Mahoney equation can be split into a system of an elliptic equation and an ordinary differential equation (ODE). For the elliptic equation, we use a classical finite difference weighted essentially non-oscillatory (WENO) scheme. For the ODE, the third order explicit Runge-Kutta method is employed to discretize the time derivative. Due to the WENO reconstruction, the splitting method shows an excellent ability in capturing the formation and propagation of shock peak on solutions. The numerical simulations for asymptotic solution of the BBM equation illustrate the capability of the method.