One-step methods for two-point boundary value problems in ordinary differential equations with parameters

Tadeusz Jankowski

Applications of Mathematics (1994)

  • Volume: 39, Issue: 2, page 81-95
  • ISSN: 0862-7940

Abstract

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A general theory of one-step methods for two-point boundary value problems with parameters is developed. On nonuniform nets h n , one-step schemes are considered. Sufficient conditions for convergence and error estimates are given. Linear or quadratic convergence is obtained by Theorem 1 or 2, respectively.

How to cite

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Jankowski, Tadeusz. "One-step methods for two-point boundary value problems in ordinary differential equations with parameters." Applications of Mathematics 39.2 (1994): 81-95. <http://eudml.org/doc/32872>.

@article{Jankowski1994,
abstract = {A general theory of one-step methods for two-point boundary value problems with parameters is developed. On nonuniform nets $h_n$, one-step schemes are considered. Sufficient conditions for convergence and error estimates are given. Linear or quadratic convergence is obtained by Theorem 1 or 2, respectively.},
author = {Jankowski, Tadeusz},
journal = {Applications of Mathematics},
keywords = {one-step methods; two-point boundary value problems; one step methods; two-point boundary value problem; first-order system; convergence},
language = {eng},
number = {2},
pages = {81-95},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {One-step methods for two-point boundary value problems in ordinary differential equations with parameters},
url = {http://eudml.org/doc/32872},
volume = {39},
year = {1994},
}

TY - JOUR
AU - Jankowski, Tadeusz
TI - One-step methods for two-point boundary value problems in ordinary differential equations with parameters
JO - Applications of Mathematics
PY - 1994
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 39
IS - 2
SP - 81
EP - 95
AB - A general theory of one-step methods for two-point boundary value problems with parameters is developed. On nonuniform nets $h_n$, one-step schemes are considered. Sufficient conditions for convergence and error estimates are given. Linear or quadratic convergence is obtained by Theorem 1 or 2, respectively.
LA - eng
KW - one-step methods; two-point boundary value problems; one step methods; two-point boundary value problem; first-order system; convergence
UR - http://eudml.org/doc/32872
ER -

References

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  2. Computation and theory in ordinary differential equations, W.H. Freeman, San Francisco, 1970. (1970) MR0267765
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  4. 10.1002/mana.19861250103, Math. Nachr. 125 (1986), 7-28. (1986) MR0847349DOI10.1002/mana.19861250103
  5. One-step methods for ordinary differential equations with parameters, Apl. Mat. 35 (1990), 67-83. (1990) Zbl0701.65053MR1039412
  6. On the convergence of multistep methods for nonlinear two-point boundary value problems, APM (1991), 185–200. (1991) Zbl0746.65060MR1109587
  7. Numerical methods for two point boundary value problems, Waltham, Blaisdell, 1968. (1968) Zbl0172.19503MR0230476
  8. Numerical solution of two-point boundary value problems, Society for Industrial and Applied Mathematics, Philadelphia 24, 1976. (1976) MR0433897
  9. Un procedimento di calcolo connesso ad un noto problema ai limiti per l’equazione x ˙ = f ( t , x , λ ) , Mathematiche 23 (1968), 319-328. (1968) MR0267785
  10. 10.1002/zamm.19760560806, ZAMM 56 (1976), 387-388. (1976) Zbl0338.34019MR0430389DOI10.1002/zamm.19760560806
  11. A multipoint boundary value problem with a parameter for systems of differential equations in Banach space, Sibirski Math. Z. 9 (1968), 223-228. (Russian) (1968) MR0281987
  12. Introduction to numerical analysis, Springer-Verlag, New York, 1980. (1980) MR0557543

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