Two-step methods and bi-orthogonality

Iserles, A.; Nørsett, S. P.

doi:10.1090/S0025-5718-1987-0906187-8

Two-step methods and bi-orthogonality
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by A. Iserles and S. P. Nørsett PDF

Math. Comp. 49 (1987), 543-552 Request permission

Abstract:

We study order and zero-stability of two-step methods of Obrechkoff type for ordinary differential equations. A relation between order and properties of mth degree polynomials orthogonal to ${x^{{\mu _i}}}$, $1 \leqslant i \leqslant m$, where $- 1 < {\mu _1} < {\mu _2} < \cdots < {\mu _m}$, is established. These polynomials are investigated, focusing on their explicit form, Rodrigues-type formulae and loci of their zeros.

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