Conservative compact difference scheme based on the scalar auxiliary
variable method for the generalized Kawahara equation
Abstract
In this paper, a conservative compact difference scheme for the
generalized Kawahara equation is constructed based on the scalar
auxiliary variable (SAV) approach. The discrete conservative laws of
mass and Hamiltonian energy and boundedness estimates are studied in
detail. The error estimates in discrete
$L^{\infty}$-norm and $L^2$-norm of the
presented scheme are analyzed by using the discrete energy method. We
give an efficiently algorithm of the presented scheme which only needs
to solve two decoupled equations.