Asymptotic error expansions for stiff equations: Applications
In various previous papers the authors have studied the structure of the global discretization error for: the implicit Euler method [SIAM J. Numer. Anal. 27, 67-104 (1990; reviewed above)], the implicit midpoint rule and the implicit trapezoidal rule [Numer. Math. 56, 469-499 (1989; Zbl 0684.65075) and Report Nr. 77/88, Inst. für Angewandte und Numerische Mathematik, TU Wien (1988)], all applied to a general class of nonlinear stiff initial value problems. In the present paper the last results, even the asymptotically incorrect ones, are proved to be useful for an analysis of two acceleration techniques: extrapolation, both in strongly and in mildly stiff cases, and defect correction. Numerical results are discussed.
scientific article; zbMATH DE number 4128328