A collocation formulation of multistep methods for variable step-size extensions

Summary, in English

Multistep methods are classically constructed by specially designed difference operators on an equidistant time grid. To make them practically useful, they have to be implemented by varying the step-size according to some error-control algorithm. It is well known how to extend Adams and BDF formulas to a variable step-size formulation. In this paper we present a collocation approach to construct variable step-size formulas. We make use of piecewise polynomials to show that every k-step method of order k + I has a variable step-size polynomial collocation formulation. (C) 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.

• Författare: Carmen Arévalo; Claus Führer; M Selva
• Avdelning/ar: Matematik LTH; Numerical Analysis
• Publiceringsår: 2002
• Språk: Engelska
• Sidor: 5-16
• Publikation/Tidskrift/Serie: Applied Numerical Mathematics
• Volym: 42
• Issue: 1-3
• Länkar: http://dx.doi.org/10.1016/S0168-9274(01)00138-6
• Dokumenttyp: Artikel i tidskrift
• Förlag: Elsevier
• Ämne: Mathematics
• Nyckelord: step-size formulas; variable; ordinary differential equations (ODEs); multistep methods; collocation
• Status: Published
• Forskningsgrupp: Numerical Analysis
• ISBN/ISSN/Övrigt: ISSN: 0168-9274