Periodic Behaviors of a Linear Fourth-Order Difference Solution to the Benjamin–Bona–Mahony-Type Equation with Time-Periodic Boundaries

Abstract

The periodic behaviors of a linear fourth-order difference solution to the Benjamin–Bona–Mahony (BBM)-type equation with time-periodic boundaries are analyzed in this paper. Firstly, we employ a variable transformation to change the original BBM-type equation with time-periodic boundaries into a new BBM-type equation with zero boundaries. We then construct a fourth-order linear finite difference method to discrete the new BBM-type equation. The solvability, convergence, stability and accuracy of the approximating solution are discussed. The computation procedure of the present method is given in detail. Numerical results show that the proposed difference method is reliable and efficient for time-periodic simulation.