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Finite difference calculus invariant structure of a class of algorithms for the nonlinear Klein-Gordon equation. (English) Zbl 0847.65062
The authors present an analysis of nonlinear stability of a class of invariant-conserving algorithms within the context of exact finite difference calculus. Discrete invariant expressions corresponding to each of the proposed algorithms are derived. Some numerical experiments are presented to illustrate the conservation property of the proposed algorithms.

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
35L65 Hyperbolic conservation laws
35L70 Second-order nonlinear hyperbolic equations
35Q53 KdV equations (Korteweg-de Vries equations)
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