Equivalent forms of multistep formulas

Author:
Robert D. Skeel

Journal:
Math. Comp. **33** (1979), 1229-1250

MSC:
Primary 65L05

DOI:
https://doi.org/10.1090/S0025-5718-1979-0537967-4

Corrigendum:
Math. Comp. **47** (1986), 769.

MathSciNet review:
537967

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Abstract | References | Similar Articles | Additional Information

Abstract: For uniform meshes it is shown that any linear *k*-step formula can be formulated so that only *k* values need to be saved between steps. By saving additional *m* values it is possible to construct local polynomial approximations of degree , which can be used as predictor formulas. Different polynomial bases lead to different equivalent forms of multistep formulas. In particular, local monomial bases yield Nordsieck formulas. An explicit one-to-one correspondence is established between Nordsieck formulas and *k*-step formulas of order at least *k*, and a strong equivalence result is proved for all but certain pathological cases. Equivalence is also shown for P(EC) formulas but not for P(EC)E formulas.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1979-0537967-4

Keywords:
Linear multistep formula,
multistep formula,
linear multistep method,
multistep method,
Nordsieck method,
multivalue method,
predictor-corrector method

Article copyright:
© Copyright 1979
American Mathematical Society