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Title: On numerical solution of ordinary differential equations with discontinuities (English)
Author: Jankowski, Tadeusz
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 33
Issue: 6
Year: 1988
Pages: 487-492
Summary lang: English
Summary lang: Russian
Summary lang: Czech
Category: math
Summary: The author defines the numerical solution of a first order ordinary differential equation on a bounded interval in the way covering the general form of the so called one-step methods, proves convergence of the method (without the assumption of continuity of the righthad side) and gives a sufficient condition for the order of convergence to be $O(h^v)$. (English)
Keyword: discontinuities
Keyword: system
Keyword: one-step method
Keyword: convergence
Keyword: order of convergence
Keyword: numerical solution of differential equations
MSC: 34A34
MSC: 65L05
idZBL: Zbl 0671.65061
idMR: MR0973242
DOI: 10.21136/AM.1988.104326
Date available: 2008-05-20T18:35:40Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] I. Babuška M. Práger E. Vitásek: Numerical processes in differential equations.SNTL, Praha 1966. MR 0223101
Reference: [2] B. A. Chartres R. S. Stepleman: Actual order of convergence of Runge-Kutta methods on differential equations with discontinuities.SIAM J. Numer. Anal. 11 (1974), 1193-1206. MR 0381316, 10.1137/0711090
Reference: [3] E. A. Coddington N. Levinson: Theory of ordinary differential equations.Mc Graw-Hill, New York 1955. MR 0069338
Reference: [4] A. Feldstein R. Goodman: Numerical solution of ordinary and retardea differential equations with discontinuous derivatives.Numer. Math. 21 (1973), 1-13. MR 0381320, 10.1007/BF01436181
Reference: [5] P. Henrici: Discrete variable methods in ordinary differential equations.J. Wiley, New York 1968. MR 0135729
Reference: [6] T. Jankowski: Some remarks on numerical solution of initial problems for systems of differential equations.Apl. Mat. 24 (1979), 421 - 426. Zbl 0447.65039, MR 0547045
Reference: [7] T. Jankowski: On the convergence of multistep methods for ordinary differential equations with discontinuities.Demostratio Math. 16 (1983), 651 - 675. Zbl 0571.65065, MR 0733727
Reference: [8] D. P. Squier: One-step methods for ordinary differential equations.Numer. Math. 13 (1969), 176-179. Zbl 0182.21901, MR 0247773, 10.1007/BF02163235
Reference: [9] J. Szarski: Differential inequalities.PWN- Polish. Scient. Publ., Warsaw 1967. Zbl 0177.39203


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