Convergence of numerical methods for systems of neutral functional-differential-algebraic equations

Tadeusz Jankowski; Marian Kwapisz

Applications of Mathematics (1995)

  • Volume: 40, Issue: 6, page 457-472
  • ISSN: 0862-7940

Abstract

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A general class of numerical methods for solving initial value problems for neutral functional-differential-algebraic systems is considered. Necessary and sufficient conditions under which these methods are consistent with the problem are established. The order of consistency is discussed. A convergence theorem for a general class of methods is proved.

How to cite

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Jankowski, Tadeusz, and Kwapisz, Marian. "Convergence of numerical methods for systems of neutral functional-differential-algebraic equations." Applications of Mathematics 40.6 (1995): 457-472. <http://eudml.org/doc/32932>.

@article{Jankowski1995,
abstract = {A general class of numerical methods for solving initial value problems for neutral functional-differential-algebraic systems is considered. Necessary and sufficient conditions under which these methods are consistent with the problem are established. The order of consistency is discussed. A convergence theorem for a general class of methods is proved.},
author = {Jankowski, Tadeusz, Kwapisz, Marian},
journal = {Applications of Mathematics},
keywords = {neutral functional-differential-algebraic systems; consistency; convergence; consistency; convergence; initial value problems; neutral functional differential-algebraic equations; index 1},
language = {eng},
number = {6},
pages = {457-472},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Convergence of numerical methods for systems of neutral functional-differential-algebraic equations},
url = {http://eudml.org/doc/32932},
volume = {40},
year = {1995},
}

TY - JOUR
AU - Jankowski, Tadeusz
AU - Kwapisz, Marian
TI - Convergence of numerical methods for systems of neutral functional-differential-algebraic equations
JO - Applications of Mathematics
PY - 1995
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 40
IS - 6
SP - 457
EP - 472
AB - A general class of numerical methods for solving initial value problems for neutral functional-differential-algebraic systems is considered. Necessary and sufficient conditions under which these methods are consistent with the problem are established. The order of consistency is discussed. A convergence theorem for a general class of methods is proved.
LA - eng
KW - neutral functional-differential-algebraic systems; consistency; convergence; consistency; convergence; initial value problems; neutral functional differential-algebraic equations; index 1
UR - http://eudml.org/doc/32932
ER -

References

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  10. 10.1137/0721036, SIAM J. Numer. Anal. 21 (1984), 486–511. (1984) Zbl0562.65056MR0744170DOI10.1137/0721036
  11. Convergence of waveform relaxation methods for differential algebraic systems, SIAM J. Numer. Anal., In press. MR1427465
  12. Existence, uniqueness and approximate solutions of problems with a parameter, Zesz. Nauk. Politech. Gdańsk, Mat. 16 (1993), 3–167. (1993) Zbl0893.34062
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  14. 10.1137/0708072, SIAM J. Numer. Anal. 8 (1971), 786–795. (1971) Zbl0231.65070MR0295617DOI10.1137/0708072

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