Equivalent Forms of Multistep Formulas
نویسندگان
چکیده
For uniform meshes it is shown that any linear fc-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 k + m — 1, 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 fc-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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