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Finite-difference schemes for nonlinear wave equation that inherit energy conservation property. (English) Zbl 0989.65099

The author proposes two general finite-difference conservative schemes. They are applicable to many equations in one space dimension: nonlinear Klein-Gordon, nonlinear string vibration, Shimoji-Kaway and Ebihara equations. The basic property of the procedure is a rigorous discretization of variational dervatives using summation by parts. The results are compared with previous schemes.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81-08 Computational methods for problems pertaining to quantum theory
35L70 Second-order nonlinear hyperbolic equations
35Q40 PDEs in connection with quantum mechanics
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