Author(s)

Zhang Jun

Corresponding Author

Zhang Jun

ABSTRACT

In this paper, the asymptotic stability and numerical method of shallow water wave equation with Benjamin-Bona-Mahony type is considered. Under suitable assumption, we prove that the solution of the shallow water wave equation is asymptotically convergent to the steady-state solution of the equation, and some exponentially decay rate are obtained. In addition, we also construct a numerical scheme of the equation, we prove that the scheme is unconditionally stable, and we also get the estimate of the full discrete scheme. Finally, some results of the theoretical analysis are verified by numerical experiments

KEYWORDS

BBM type equation, Asymptotic stability analysis, Exponential decay, Unconditional stability, Error estimate