On numerical solution of ordinary differential equations with discontinuities

Tadeusz Jankowski

Aplikace matematiky (1988)

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

Abstract

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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 ) .

How to cite

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Jankowski, 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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  1. I. Babuška M. Práger E. Vitásek, Numerical processes in differential equations, SNTL, Praha 1966. (1966) Zbl0156.16003MR0223101
  2. B. A. Chartres R. S. Stepleman, 10.1137/0711090, SIAM J. Numer. Anal. 11 (1974), 1193-1206. (1974) Zbl0292.65038MR0381316DOI10.1137/0711090
  3. E. A. Coddington N. Levinson, Theory of ordinary differential equations, Mc Graw-Hill, New York 1955. (1955) Zbl0064.33002MR0069338
  4. A. Feldstein R. Goodman, 10.1007/BF01436181, Numer. Math. 21 (1973), 1-13. (1973) Zbl0266.65056MR0381320DOI10.1007/BF01436181
  5. P. Henrici, Discrete variable methods in ordinary differential equations, J. Wiley, New York 1968. (1968) Zbl0112.34901MR0135729
  6. T. Jankowski, Some remarks on numerical solution of initial problems for systems of differential equations, Apl. Mat. 24 (1979), 421 - 426. (1979) Zbl0447.65039MR0547045
  7. T. Jankowski, On the convergence of multistep methods for ordinary differential equations with discontinuities, Demostratio Math. 16 (1983), 651 - 675. (1983) Zbl0571.65065MR0733727
  8. D. P. Squier, 10.1007/BF02163235, Numer. Math. 13 (1969), 176-179. (1969) Zbl0182.21901MR0247773DOI10.1007/BF02163235
  9. J. Szarski, Differential inequalities, PWN- Polish. Scient. Publ., Warsaw 1967. (1967) Zbl0177.39203

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