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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Construction of variable-stepsize multistep formulas


Author: Robert D. Skeel
Journal: Math. Comp. 47 (1986), 503-510, S45
MSC: Primary 65L05
MathSciNet review: 856699
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Abstract: A systematic way of extending a general fixed-stepsize multistep formula to a minimum storage variable-stepsize formula has been discovered that encompasses fixed-coefficient (interpolatory), variable-coefficient (variable step), and fixed leading coefficient as special cases. In particular, it is shown that the "interpolatory" stepsize changing technique of Nordsieck leads to a truly variable-stepsize multistep formula (which has implications for local error estimation and formula changing), and it is shown that the "variable-step" stepsize changing technique applicable to the Adams and backward-differentiation formulas has a reasonable generalization to the general multistep formula. In fact, it is shown how to construct a variable-order family of variable-coefficient formulas. Finally, it is observed that the first Dahlquist barrier does not apply to adaptable multistep methods if storage rather than stepnumber is the key consideration.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1986-0856699-X
PII: S 0025-5718(1986)0856699-X
Keywords: Multistep formula, multistep method, multivalue method, variable stepsize, variable order
Article copyright: © Copyright 1986 American Mathematical Society