Zusammenfassung
Linear k-step method (k ≥ 2) with constant coefficients are derived in a “natural” way by choosing as the second characteristic polynomial a Schur polynomial whose coefficients depend on a certain set of parameters. The choice of these parameters is based on a result by Marden concerning the location of the zeros of a class of rational functions. For the (practically important) case k = 2 it is shown that the resulting class of methods is A -stable and has order p = 2. The trapezoidal rule and a class of one-step methods introduced by Lininger and Willoughby turn out to be degenerate cases of this class of two-step-methods.
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Literatur
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© 1974 Springer Basel AG
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Brunner, H. (1974). Über Klassen von A -Stabilen Linearen Mehrschrittverfahren Maximaler Ordnung. In: Albrecht, J., Collatz, L. (eds) Numerische Methoden bei Differentialgleichungen und mit funktionalanalytischen Hilfsmitteln. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 19. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6988-1_4
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DOI: https://doi.org/10.1007/978-3-0348-6988-1_4
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