Two Energy Conserving Numerical Schemes for the Klein-Gordon-Zakharov Equations

Abstract

Two new difference schemes are proposed for an initial-boundary-value problem of the Klein-Gordon-Zakharov (KGZ) equations. They have the advantage that there is a discrete energy which is conserved. Their stability and convergence of difference solutions are proved in order O($h^2+{\tau }^2$) on the basis of the prior estimates. Results of numerical experiments demonstrate the efficiency of the new schemes.