On numerical integration of implicit ordinary differential equations

Zdzisław Jackiewicz; Marian Kwapisz

Aplikace matematiky (1981)

  • Volume: 26, Issue: 2, page 97-110
  • ISSN: 0862-7940

Abstract

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In this paper it is shown how the numerical methods for ordinary differential equations can be adapted to implicit ordinary differential equations. The resulting methods are of the same order as the corresponding methods for ordinary differential equations. The convergence theorem is proved and some numerical examples are given.

How to cite

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Jackiewicz, Zdzisław, and Kwapisz, Marian. "On numerical integration of implicit ordinary differential equations." Aplikace matematiky 26.2 (1981): 97-110. <http://eudml.org/doc/15186>.

@article{Jackiewicz1981,
abstract = {In this paper it is shown how the numerical methods for ordinary differential equations can be adapted to implicit ordinary differential equations. The resulting methods are of the same order as the corresponding methods for ordinary differential equations. The convergence theorem is proved and some numerical examples are given.},
author = {Jackiewicz, Zdzisław, Kwapisz, Marian},
journal = {Aplikace matematiky},
keywords = {nonstationary quasilinear multistep methods; implicit ordinary differential equations; convergence theorem; numerical examples; nonstationary quasilinear multistep methods; implicit ordinary differential equations; convergence theorem; numerical examples},
language = {eng},
number = {2},
pages = {97-110},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On numerical integration of implicit ordinary differential equations},
url = {http://eudml.org/doc/15186},
volume = {26},
year = {1981},
}

TY - JOUR
AU - Jackiewicz, Zdzisław
AU - Kwapisz, Marian
TI - On numerical integration of implicit ordinary differential equations
JO - Aplikace matematiky
PY - 1981
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 26
IS - 2
SP - 97
EP - 110
AB - In this paper it is shown how the numerical methods for ordinary differential equations can be adapted to implicit ordinary differential equations. The resulting methods are of the same order as the corresponding methods for ordinary differential equations. The convergence theorem is proved and some numerical examples are given.
LA - eng
KW - nonstationary quasilinear multistep methods; implicit ordinary differential equations; convergence theorem; numerical examples; nonstationary quasilinear multistep methods; implicit ordinary differential equations; convergence theorem; numerical examples
UR - http://eudml.org/doc/15186
ER -

References

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  1. W. H. Enright, 10.1137/0711029, SIAM J. Numer. Anal. 11, (1974), 321-331. (1974) MR0351083DOI10.1137/0711029
  2. P. Hartman, Ordinary Differential Equations, New York-London-Sydney: J. Wiley 1964. (1964) Zbl0125.32102MR0171038
  3. P. Henrici, Discrete Variable Methods in Ordinary Differential Equations, New York: J. Wiley 1968. (1968) MR0135729
  4. Z. Jackiewicz M. Kwapisz, 10.1007/BF02252383, Computing 20, (1978), 351 - 361. (1978) MR0619909DOI10.1007/BF02252383
  5. M. Kwapisz, On the existence and uniqueness of solutions of a certain integral-functional equation, Ann. Polon. Math. 31, (1975), 23 - 41. (1975) MR0380329
  6. J. D. Lambert, Computational Methods in Ordinary Differential Equations, London-New York: J. Wiley 1973. (1973) Zbl0258.65069MR0423815
  7. L. Lapidus J. H. Seifeld, Numerical Solution of Ordinary Differential Equations, London - New York: Academic Press 1971. (1971) MR0281355
  8. 18] J. D. Mamiedow, Approximate Methods of Solution of Ordinary Differential Equations, (in Russian). Baku: Maarif 1974. (1974) 
  9. D. I. Martinjuk, 10.1093/comjnl/5.4.329, (in Russian). Kiev: Naukova Dumka 1972. (1972) MR0611163DOI10.1093/comjnl/5.4.329
  10. H. H. Rosenbrock, Some general implicit processes for the numerical solution of differential equations, Comput. J. 5 (1963), 329-330. (1963) Zbl0112.07805MR0155434

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