Asymptotic error expansions for stiff equations: Applications
Copyright policy )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.
- TU Wien Austria
implicit Euler method, Extrapolation to the limit, deferred corrections, defect correction, extrapolation, Nonlinear ordinary differential equations and systems, nonlinear stiff initial value problems, Numerical methods for initial value problems involving ordinary differential equations, global discretization error, acceleration techniques, Numerical results, implicit trapezoidal rule, asymptotic error expansion, implicit midpoint rule
implicit Euler method, Extrapolation to the limit, deferred corrections, defect correction, extrapolation, Nonlinear ordinary differential equations and systems, nonlinear stiff initial value problems, Numerical methods for initial value problems involving ordinary differential equations, global discretization error, acceleration techniques, Numerical results, implicit trapezoidal rule, asymptotic error expansion, implicit midpoint rule
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