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New conservative schemes with discrete variational derivatives for nonlinear wave equations. (English) Zbl 1120.65096
The author considers certain classes of one-dimensional nonlinear wave equations and proposes new finite difference schemes of conservative type. The wave equations are represented as systems of first order differential equations which are discretized using discrete variational derivatives to obtain families of conservative schemes. Applications are presented for the nonlinear Klein-Gordon equation and the Boussinesq equation. Numerical examples reveal the good performance of the new schemes.

65M06Finite difference methods (IVP of PDE)
35L70Nonlinear second-order hyperbolic equations
35Q53KdV-like (Korteweg-de Vries) equations
Full Text: DOI
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