Construction of variable-stepsize multistep formulas

Author:
Robert D. Skeel

Journal:
Math. Comp. **47** (1986), 503-510, S45

MSC:
Primary 65L05

DOI:
https://doi.org/10.1090/S0025-5718-1986-0856699-X

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:
https://doi.org/10.1090/S0025-5718-1986-0856699-X

Keywords:
Multistep formula,
multistep method,
multivalue method,
variable stepsize,
variable order

Article copyright:
© Copyright 1986
American Mathematical Society