Equivalent forms of multistep formulas
Author:
Robert D. Skeel
Journal:
Math. Comp. 33 (1979), 12291250
MSC:
Primary 65L05
Corrigendum:
Math. Comp. 47 (1986), 769.
MathSciNet review:
537967
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Abstract: For uniform meshes it is shown that any linear kstep 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 onetoone correspondence is established between Nordsieck formulas and kstep 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:
http://dx.doi.org/10.1090/S00255718197905379674
PII:
S 00255718(1979)05379674
Keywords:
Linear multistep formula,
multistep formula,
linear multistep method,
multistep method,
Nordsieck method,
multivalue method,
predictorcorrector method
Article copyright:
© Copyright 1979
American Mathematical Society
