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Abstract: In this paper we consider stepsize selection in one class of Adams linear multistep methods for ordinary differential equations. In particular, the exact form of the local error for a variable step method is considered and a class of new direct approximations proposed. The implications of this approach are then discussed and illustrations provided with numerical results. Intended applications include differential equations with derivative discontinuities and initial stepsize strategies. (Update)
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3.1: Experiments in stepsize control for Adams linear multistep methods - Wille (1994) (Correct)
1.4: New Stepsize Estimators for Linear Multistep Methods - Wille (1994) (Correct)
1.3: Equilibrium States for Multistep Methods - Hall (1995) (Correct)
BibTeX entry: (Update)
@misc{ will-experiments,
author = "David R. Willé",
title = "Experiments in stepsize control for Adams linear multistep methods",
url = "citeseer.ist.psu.edu/512719.html" }
Citations (may not include all citations):71 Solving ordinary differential equations I -- nonstiff proble.. (context) - Hairer, Nrsett et al. - 1987
44 Theory of functional differential equations (context) - Hale - 1977
44 Computer solution of ordinary differential equations (context) - Shampine, Gordon - 1975
11 DELSOL --- a numerical code for the solution of systems of d.. (context) - Will'e, Baker - 1992
9 The effect of changing the stepsize in linear multistep code.. (context) - Shampine, Bogacki - 1989
9 Projizierende Mehrschrittverfahren zur numerischen Losung vo.. (context) - Eich - 1991
8 Automatic selection of the initial step size for an ODE solv.. (context) - Gladwell, Shampine et al. - 1987
6 Multiple g-stop facility in ATOMFT -- a Taylor series ODE so.. (context) - Corliss, Chang - 1988
5 Changing stepsize in the integration of differential equatio.. (context) - Krogh - 1973
4 Eine effiziente Ordnungs- und Schrittweitensteuerung unter V.. (context) - Bleser - 1986
2 The numerical solution of delay-differential equations (context) - Will'e - 1989
2 the change of stepsizes in multistep codes (context) - Calvo, Montijano et al. - 1993
2 private correspondence (context) - Schwerin - 1993
1 New stepsize estimators for linear multistep methods - Will'e - 1994
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