Asymptotic error expansions for stiff equations: An analysis for the implicit midpoint and trapezoidal rules in the strongly stiff case
The structure of the global discretization error is studied for the implicit midpoint and trapezoidal rules, applied to nonlinear stiff initial value problems. In general, the global error contains rapidly oscillating terms of order \(h^ 2\). For special classes of stiff problems, it is shown that these terms also contain a factor of \(\epsilon\), where -1/\(\epsilon\) is the magnitude of the stiff eigenvalues, and thus that a ``full'' asymptotic error expansion exists in the case \(\epsilon \ll h\).
scientific article; zbMATH DE number 4121340
scientific article