Über Klassen von A -Stabilen Linearen Mehrschrittverfahren Maximaler Ordnung
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.
Unable to display preview. Download preview PDF.
- 1.Bjurel, G. et al; Survey of stiff ordinary differential equations.Report NA 70.11, Royal Institute of Technology, Stockholm, 1970.Google Scholar
- 6.Henrici, P.: Discrete Variable Methods in Ordinary Differential Equations. Wiley, New York, 1962.Google Scholar
- 9.Liniger, W. and R.A. Willoughby: Efficient numerical integration methods for stiff system of differential equations. IBM Res. Report RC-1970, 1967.Google Scholar
- 10.Marden, M.: Geometry of Polynomials (2nd ed.). Amer. Mathem. Society, Providence, 1966.Google Scholar