Preservation of Strong Stability Associated with Analytic Semigroups
نویسنده
چکیده
which is uniform with respect to λ > 0. Recall that we showed that this stability estimate is preserved by the implicit Euler method. However, the explicit Euler method is only stable provided that ∆t < 2/λ, so its stability is not uniform in λ. One consequence is that it is less efficient to compute with the explicit Euler method over long time intervals. Note that in this example, we also have a stability estimate for the derivative. Namely, |y′(t)| = λe−λt|y0| ≤ Ct−1|y0|, t > 0, (3)
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