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Two energy conserving numerical schemes for the Klein-Gordon-Zakharov equations. (English) Zbl 1397.65133

Summary: 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.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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