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Title: Some remarks on numerical solution of initial problems for systems of differential equations (English)
Author: Jankowski, Tadeusz
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 24
Issue: 6
Year: 1979
Pages: 421-426
Summary lang: English
Summary lang: Czech
Summary lang: Russian
Category: math
Summary: This paper presents a class of numerical methods for approximate solution of systems of ordinary differential equations. It is shown that under certain general conditions these methods are convergent for sufficiently small step size. We give estimations of errors which are better than the known ones. (English)
Keyword: systems
Keyword: sufficient conditions for convergence
Keyword: Gronwall inequality
Keyword: error bound
MSC: 65L05
idZBL: Zbl 0447.65039
idMR: MR0547045
DOI: 10.21136/AM.1979.103825
Date available: 2008-05-20T18:13:06Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] Babuška I., Práger M., Vitásek E.: Numerical processes in differential equations.Praha 1966. MR 0223101
Reference: [2] Hartman P.: Ordinary differential equations.New York: John Wiley and Sons 1964. Zbl 0125.32102, MR 0171038
Reference: [3] Hayoshi K.: On stability of numerical solutions of a differential system by one-step methods.TRU Mathematics 5, 67-83 (1969). MR 0269123
Reference: [4] Henrici P.: Discrete variable methods in ordinary differential equations.New York: John Wiley and Sons 1968. MR 0135729
Reference: [5] Ohashi T.: On the conditions for convergence of one-step methods for ordinary differential equations.TRU Mathematics 6, 59-62 (1970). Zbl 0252.65054, MR 0331791
Reference: [6] Squier D. P.: One-step methods for ordinary differential equations.Numer. Math. 13, 176-179 (1969). Zbl 0182.21901, MR 0247773, 10.1007/BF02163235


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