It is well known that leapfrog (explicit mid-point) discretizations of partial differential equations may have unbounded solutions for any choice of mesh-sizes, (even for choices satisfying conditions for linear stability). We provide a means for forecasting the qualitative behaviour of the computed leapfrog points, thus explaining the dynamics of the nonlinear instability phenomenon.
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J. M. Sanz‐Serna (1985) studied this question.
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