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Title: Overimplicit multistep methods (English)
Author: Práger, Milan
Author: Taufer, Jiří
Author: Vitásek, Emil
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 18
Issue: 6
Year: 1973
Pages: 399-421
Summary lang: English
Summary lang: Czech
Category: math
Summary: The paper is concerned with the numerical solution of ordinary differential equations by a new class of methods called overimplicit multistep methods. The effort is devoted to the study of the convergence and $A$-stability of the introduced methods. $A$-stable formulae of arbitrarily high orders are shown to exist in this new class. This implies the efficiency of using these methods for stiff problems. ()
MSC: 65J99
MSC: 65L05
idZBL: Zbl 0298.65052
idMR: MR0366041
DOI: 10.21136/AM.1973.103497
Date available: 2008-05-20T17:57:25Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] I. Babuška M. Práger, E. Vitásek: Numerical processes in differential equations.Interscience publishers, London, New York, Sydney (1966). MR 0223101
Reference: [2] G. Birkhoff, R. S. Varga: Discretization errors for well-set Cauchy problems I.J. Math, and Phys. 44 (1965), 1-23. Zbl 0134.13406, MR 0179952, 10.1002/sapm19654411
Reference: [3] G. Dahlquist: A special stability problem for linear multistep methods.BIT 3 (1963), 27-43. Zbl 0123.11703, MR 0170477, 10.1007/BF01963532
Reference: [4] F. R. Gantmacher (Ф. Р. Гантмахер): Теория матриц.Наука, Москва (1966). Zbl 0136.00410
Reference: [5] P. Henrici: Discrete variable methods in ordinary differential equations.J. Wiley & Sons, Inc., New York, London (1962). Zbl 0112.34901, MR 0135729
Reference: [6] J. Taufer (И. Тауфер): Об одном обобщенном многошаговом методе, сб. Применение функциональных методов к краевым задачам математической физики.Новосибирск (1972). Zbl 0262.65050
Reference: [7] R. S. Varga: Matrix iterative analysis.Prentice-Hall, Inc., Englewood Cliffs, New Jersey (1962). MR 0158502
Reference: [8] E. Vitásek (E. Витасек): Строго неявные методы для решения дифференциальных уравнений.сб. Применение функциональных методов к краевым задачам математической физики, Новосибирск (1972).


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