[Zurück]

W. Auzinger, R. Frank:
"Asymptotic error expansions for stiff equations: An analysis for the implicit midpoint and trapezoidal rules in the strongly stiff case";
Numerische Mathematik, 56 (1989), S. 469 - 499.

The structure of the global discretization error is studied for the implicit midpoint and trapezoidal rules applied to nonlinear stiff initial value problems. The point is that, in general, the globalerror contains nonsmooth (oscillating) terms at the dominant O(h^2)-level. However, it is shown in the present paper that for special classes of stiff problems these nonsmooth terms contain an additional factor \epsilon (where -1/\epsilon is the magnitude of the stiff eigenvalues). In these cases a `full' asymptotic error expansion exists in the strongly stiff case \epsilon sufficiently small compared to the stepsize h).

http://dx.doi.org/10.1007/BF01396649