A careful analysis of the multioperational finite difference schemes proposed by Leendertse reveals a nonlinear numerical instability. This instability arises from the imperfect time centering of certain nonlinear terms in the shallow water equations. For many applications, the natural damping due to the friction term controls or masks the instability. The results of the stability analysis suggest that the instability becomes uncontrollable when a small grid spacing is used. These conclusions are confirmed by numerical experiment.
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T. J. Weare (1976) studied this question.
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