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

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Author

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.

Department/s

Publishing year

2002

Language

English

Pages

5-16

Publication/Series

Applied Numerical Mathematics

Volume

42

Issue

1-3

Document type

Journal article

Publisher

Elsevier

Topic

  • Mathematics

Keywords

  • step-size formulas
  • variable
  • ordinary differential equations (ODEs)
  • multistep methods
  • collocation

Status

Published

Research group

  • Numerical Analysis

ISBN/ISSN/Other

  • ISSN: 0168-9274