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.