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Two-step methods and bi-orthogonality

Authors: A. Iserles and S. P. Nørsett
Journal: Math. Comp. 49 (1987), 543-552
MSC: Primary 65L05; Secondary 33A65
MathSciNet review: 906187
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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.

References [Enhancements On Off] (What's this?)

  • [1] A. Iserles, "Two-step numerical methods for parabolic differential equations," BIT, v. 21, 1981, pp. 80-96. MR 616702 (83i:65065)
  • [2] A. Iserles & S. P. Nørsett, "Bi-orthogonal polynomials," in Orthogonal Polynomials and Their Applications (A. Draux, A. Magnus and P. Maroni, eds.), Lecture Notes in Math., vol. 1171, Springer-Verlag, Berlin, 1985, pp. 92-100. MR 838964 (87f:00023)
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Article copyright: © Copyright 1987 American Mathematical Society

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