One-step methods for ordinary differential equations with parameters

Tadeusz Jankowski

Aplikace matematiky (1990)

  • Volume: 35, Issue: 1, page 67-83
  • ISSN: 0862-7940

Abstract

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In the present paper we are concerned with the problem of numerical solution of ordinary differential equations with parameters. Our method is based on a one-step procedure for IDEs combined with an iterative process. Simple sufficient conditions for the convergence of this method are obtained. Estimations of errors and some numerical examples are given.

How to cite

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Jankowski, Tadeusz. "One-step methods for ordinary differential equations with parameters." Aplikace matematiky 35.1 (1990): 67-83. <http://eudml.org/doc/15611>.

@article{Jankowski1990,
abstract = {In the present paper we are concerned with the problem of numerical solution of ordinary differential equations with parameters. Our method is based on a one-step procedure for IDEs combined with an iterative process. Simple sufficient conditions for the convergence of this method are obtained. Estimations of errors and some numerical examples are given.},
author = {Jankowski, Tadeusz},
journal = {Aplikace matematiky},
keywords = {ordinary differential equations with parameters; numerical solution; one-step method; parameter estimation; iterative methods; convergence; error estimates; numerical examples; one-step methods; parameter estimation; parameters; nonlinear; Iterative methods; convergence; error estimates; Numerical examples},
language = {eng},
number = {1},
pages = {67-83},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {One-step methods for ordinary differential equations with parameters},
url = {http://eudml.org/doc/15611},
volume = {35},
year = {1990},
}

TY - JOUR
AU - Jankowski, Tadeusz
TI - One-step methods for ordinary differential equations with parameters
JO - Aplikace matematiky
PY - 1990
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 35
IS - 1
SP - 67
EP - 83
AB - In the present paper we are concerned with the problem of numerical solution of ordinary differential equations with parameters. Our method is based on a one-step procedure for IDEs combined with an iterative process. Simple sufficient conditions for the convergence of this method are obtained. Estimations of errors and some numerical examples are given.
LA - eng
KW - ordinary differential equations with parameters; numerical solution; one-step method; parameter estimation; iterative methods; convergence; error estimates; numerical examples; one-step methods; parameter estimation; parameters; nonlinear; Iterative methods; convergence; error estimates; Numerical examples
UR - http://eudml.org/doc/15611
ER -

References

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  1. I. Babuška M. Práger E. Vitásek, Numerical processes in differential equations, Praha 1966. (1966) MR0223101
  2. R. Conti, Problemes lineaires pour les équations differentialles ordinaires, Math. Nachr. 23 (1961), 161-178. (1961) MR0138818
  3. J. W. Daniel R. E. Moore, Computation and theory in ordinary differential equations, San Francisco 1970. (1970) MR0267765
  4. 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
  5. P. Henrici, Discrete variable methods in ordinary differential equations, John Wiley, New York 1962. (1962) Zbl0112.34901MR0135729
  6. T. Jankowski M. Kwapisz, 10.1002/mana.19760710119, Math. Nachr. 71 (1976), 237-247. (1976) MR0405190DOI10.1002/mana.19760710119
  7. H. B. Keller, Numerical methods for two-point boundary-value problems, Blaisdell, London 1968. (1968) Zbl0172.19503MR0230476
  8. A. V. Kibenko A. I. Perov, A two-point boundary value problem with parameter, (Russian), Azerbaidzan. Gos. Univ. Učen. Zap. Ser. Fiz.-Mat. i Him. Nauka 3 (1961), 21 - 30. (1961) MR0222376
  9. J. Lambert, Computational methods in ordinary differential equations, London 1973. (1973) Zbl0258.65069MR0423815
  10. A. 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
  11. Z. B. Seidov, A multipoint boundary value problem with a parameter for systems of differential equations in Banach space, (Russian). Sibirski Math. Z. 9 (1968), 223 - 228. (1968) MR0281987
  12. J. Stoer R. Bulirsch, Introduction to numerical analysis, New York, Heidelberg, Berlin 1980. (1980) MR0578346
  13. H. J. Stetter, Analysis of discretization methods for ordinary differential equations, New York, Heidelberg, Berlin 1973. (1973) Zbl0276.65001MR0426438
  14. K. Zawischa, 10.1007/BF01696760, Monatsh. Math. Phys. 37 (1930), 103-124. (1930) MR1549778DOI10.1007/BF01696760

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