| Title | A collocation formulation of multistep methods for variable step-size extensions |
| Authors | Carmen Arévalo, Claus Führer, M Selva |
| Alternative Location | http://dx.doi.org/10.1016/S..., Restricted Access |
| Publication | Applied Numerical Mathematics |
| Year | 2002 |
| Volume | 42 |
| Issue | 1-3 |
| Pages | 5 - 16 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Elsevier |
| Abstract 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. |
| Keywords | step-size formulas, variable, ordinary differential equations (ODEs), multistep methods, collocation, |
| ISBN/ISSN/Other | ISSN: 0168-9274 |
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