New energy-preserving schemes for Klein–Gordon–Schrödinger equations

•We consider an infinite dimensional Hamilton form of KGS equations.•We discretize spatial derivatives by Sinc collocation method then discretize derived ODEs by discrete gradient method.•New energy-preserving schemes are proposed with 1st and 2nd accuracy in time direction.•Schemes preserve discrete charge.

In this manuscript, we focus on new conservative numerical methods for Klein–Gordon–Schrödinger equations. By expressing Klein–Gordon–Schrödinger equations in an infinite-dimensional Hamiltonian form, we firstly discretize spatial derivatives by using Sinc collocation method then approximate the associated semi-discrete ordinary differential equations by discrete gradient method. Based on two different discrete gradients, two new energy-preserving schemes are provided, respectively. Furthermore, it is proved that both schemes preserve the discrete charge conservation law as well. Finally, numerical experiments are presented to show the excellent long-time conservation behavior and efficiency of the new energy-preserving schemes.