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

• 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.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

step-size formulas

variable

ordinary differential equations (ODEs)

multistep methods

collocation

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