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Convergence of an energy-preserving scheme for the Zakharov equations in one space dimension. (English) Zbl 0746.65066
An energy-preserving, linearly implicit finite difference scheme is presented for approximating solutions to the problem: \(iE_ t+E_{xx}=NE\), \(N_{tt}-N_{xx}=(| E|^ 2)_{xx}\), \(E(x,0)=E^ 0(x)\), \(N(x,0)=N^ 0(x)\), \(N_ t(x,0)=N^ 1(x)\). First- order convergence estimates are obtained in a standard “energy” norm in terms of the initial errors and usual discretization errors.
Reviewer: L.G.Vulkov (Russe)

MSC:
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L70 Second-order nonlinear hyperbolic equations
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