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Zbl 0790.65101
Vu-Quoc, Loc; Li, Shaofan
Invariant-conserving finite difference algorithms for the nonlinear Klein-Gordon equation. (English)
[J] Comput. Methods Appl. Mech. Eng. 107, No.3, 341-391 (1993). ISSN 0045-7825

A formalism to derive second-order invariant-conserving finite difference algorithms for the nonlinear Klein-Gordon equation is presented. Three algorithms are proposed which conserve in discrete form either the total energy or the momentum.\par A geometric interpretation of the algorithms is given and their stability and accuracy are investigated. An efficient solution procedure is discussed for the computer implementation of the proposed algorithms and several numerical examples are presented, which include collisions of solitary waves to demonstrate the conservation and robustness properties of those algorithms.
[Z.D\D{z}ygadło (Warszawa)]

MSC 2000:: *65Z05 Applications to physics
65M06 Finite difference methods (IVP of PDE)
65M12 Stability and convergence of numerical methods (IVP of PDE)
81Q05 Closed and approximate solutions to quantum-mechanical equations
35Q53 KdV-like equations

Keywords: second-order invariant-conserving finite difference algorithms; nonlinear Klein-Gordon equation; algorithms; stability; numerical examples; collisions of solitary waves

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