# On numerical solution of ordinary differential equations with discontinuities

Aplikace matematiky (1988)

- Volume: 33, Issue: 6, page 487-492
- ISSN: 0862-7940

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topJankowski, Tadeusz. "On numerical solution of ordinary differential equations with discontinuities." Aplikace matematiky 33.6 (1988): 487-492. <http://eudml.org/doc/15558>.

@article{Jankowski1988,

abstract = {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 $O(h^v)$.},

author = {Jankowski, Tadeusz},

journal = {Aplikace matematiky},

keywords = {discontinuities; system; one-step method; convergence; order of convergence; numerical solution of differential equations; discontinuities; system; one-step method; convergence; order of convergence},

language = {eng},

number = {6},

pages = {487-492},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {On numerical solution of ordinary differential equations with discontinuities},

url = {http://eudml.org/doc/15558},

volume = {33},

year = {1988},

}

TY - JOUR

AU - Jankowski, Tadeusz

TI - On numerical solution of ordinary differential equations with discontinuities

JO - Aplikace matematiky

PY - 1988

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 33

IS - 6

SP - 487

EP - 492

AB - 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 $O(h^v)$.

LA - eng

KW - discontinuities; system; one-step method; convergence; order of convergence; numerical solution of differential equations; discontinuities; system; one-step method; convergence; order of convergence

UR - http://eudml.org/doc/15558

ER -

## References

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- E. A. Coddington N. Levinson, Theory of ordinary differential equations, Mc Graw-Hill, New York 1955. (1955) MR0069338
- A. Feldstein R. Goodman, 10.1007/BF01436181, Numer. Math. 21 (1973), 1-13. (1973) MR0381320DOI10.1007/BF01436181
- P. Henrici, Discrete variable methods in ordinary differential equations, J. Wiley, New York 1968. (1968) MR0135729
- T. Jankowski, Some remarks on numerical solution of initial problems for systems of differential equations, Apl. Mat. 24 (1979), 421 - 426. (1979) Zbl0447.65039MR0547045
- T. Jankowski, On the convergence of multistep methods for ordinary differential equations with discontinuities, Demostratio Math. 16 (1983), 651 - 675. (1983) Zbl0571.65065MR0733727
- D. P. Squier, 10.1007/BF02163235, Numer. Math. 13 (1969), 176-179. (1969) Zbl0182.21901MR0247773DOI10.1007/BF02163235
- J. Szarski, Differential inequalities, PWN- Polish. Scient. Publ., Warsaw 1967. (1967) Zbl0177.39203

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