Conservative compact difference scheme based on the scalar auxiliary variable method for the generalized Kawahara equation

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 infinity$$ {L}<^>{\infty } $$-norm and L2$$ {L}<^>2 $$-norm of the presented scheme are analyzed by using the mathematical induction and discrete energy method. We give an efficient algorithm of the presented scheme, which only needs to solve two decoupled equations.