Convergence of multistep methods for systems of ordinary differential equations with parameters

Tadeusz Jankowski

Aplikace matematiky (1987)

  • Volume: 32, Issue: 4, page 257-270
  • ISSN: 0862-7940

Abstract

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The author considers the convergence of quasilinear nonstationary multistep methods for systems of ordinary differential with parameters. Sufficient conditions for their convergence are given. The new numerical method is tested for two examples and it turns out to be a little better than the Hamming method.

How to cite

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Jankowski, Tadeusz. "Convergence of multistep methods for systems of ordinary differential equations with parameters." Aplikace matematiky 32.4 (1987): 257-270. <http://eudml.org/doc/15498>.

@article{Jankowski1987,
abstract = {The author considers the convergence of quasilinear nonstationary multistep methods for systems of ordinary differential with parameters. Sufficient conditions for their convergence are given. The new numerical method is tested for two examples and it turns out to be a little better than the Hamming method.},
author = {Jankowski, Tadeusz},
journal = {Aplikace matematiky},
keywords = {quasilinear nonstationary multistep methods; convergence; Hamming method; Quasilinear nonstationary multistep methods; convergence},
language = {eng},
number = {4},
pages = {257-270},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Convergence of multistep methods for systems of ordinary differential equations with parameters},
url = {http://eudml.org/doc/15498},
volume = {32},
year = {1987},
}

TY - JOUR
AU - Jankowski, Tadeusz
TI - Convergence of multistep methods for systems of ordinary differential equations with parameters
JO - Aplikace matematiky
PY - 1987
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 32
IS - 4
SP - 257
EP - 270
AB - The author considers the convergence of quasilinear nonstationary multistep methods for systems of ordinary differential with parameters. Sufficient conditions for their convergence are given. The new numerical method is tested for two examples and it turns out to be a little better than the Hamming method.
LA - eng
KW - quasilinear nonstationary multistep methods; convergence; Hamming method; Quasilinear nonstationary multistep methods; convergence
UR - http://eudml.org/doc/15498
ER -

References

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  2. R. Conti, 10.1002/mana.1961.3210230304, Mathematische Nachrichten 23 (1961), 161-178. (1961) MR0138818DOI10.1002/mana.1961.3210230304
  3. A. Gasparini A. Mangini, Sul calcolo numerico delle soluzioni di un noto problema ai limiti per l’equazione y ' = λ f ( x , y ) , Le Matematiche 22 (1965), 101-121. (1965) MR0191098
  4. R. W. Hamming, 10.1145/320954.320958, Journal of the Association for Computing Machinery, t. 6 nr. 1 (1959), 37-47. (1959) Zbl0086.11201MR0102179DOI10.1145/320954.320958
  5. Z. Jackiewicz M. Kwapisz, 10.1007/BF02252383, Computing 20 (1978), 351 - 361. (1978) MR0619909DOI10.1007/BF02252383
  6. K. Jankowska T. Jankowski, On a boundary-value problem of a differential equation with a deviated argument, (Polish), Zeszyty Naukowe Politechniki Gdańskiej, Matematyka 7 (1973), 33-48. (1973) 
  7. T. Jankowski, 10.1515/dema-1983-0309, Demonstratio Mathematica 16 (1983), 651 - 675. (1983) Zbl0571.65065MR0733727DOI10.1515/dema-1983-0309
  8. T. Jankowski M. Kwapisz, 10.1002/mana.19760710119, Mathematische Nachrichten 71 (1976), 237-247. (1976) MR0405190DOI10.1002/mana.19760710119
  9. H. Jeffreys B. S. Jeffreys, Methods of mathematical physics, Cambridge UP 1956. (1956) MR0074466
  10. A. V. Kibenko A. I. Perov, A two-point boundary value problem with parameter, (Russian), Azerbaidžan. Gos. Univ. Učen. Zap. Ser. Fiz.-Mat. i Him. Nauk 3 (1961), 21-30. (1961) MR0222376
  11. J. D. Lambert, Computational methods in ordinary differential equations, New York 1973. (1973) Zbl0258.65069MR0423815
  12. D. I. Martiniuk, Lectures on qualitative theory of difference equations, (Russian). Kiev: Naukova Dumka 1972. (1972) MR0611163
  13. R. Pasquali, Un procedimento di calcolo connesso ad un noto problema ai limiti per l’equazione x ' = f ( t , x , λ ) , Le Matematiche 23 (1968), 319-328. (1968) Zbl0182.22003MR0267785
  14. Z. B. Seidov, A multipoint boundary value problem with a parameter for systems of differential equations in Banach space, Sibirskij Matematiczeskij Žurnał 9 (1968), 223-228. (1968) MR0281987
  15. D. Squier, 10.1016/0021-9045(68)90027-0, Journal of Approximation Theory 1 (1968), 236-242. (1968) Zbl0219.39003MR0234637DOI10.1016/0021-9045(68)90027-0
  16. J. Stoer R. Bulirsch, Einführung in die Numerische Mathematik I:, Springer Verlag Berlin Heidelberg 1972. (1972) MR0400617
  17. S. Takahashi, Die Differentialgleichung y ' = k f ( x , y ) , Tôhoku Math. J. 34 (1941), 249-256. (1941) 

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