Quadratic convergence of monotone iterations of differential-algebraic equations

Anita Dąbrowicz-Tlałka; Tadeusz Jankowski

Mathematica Slovaca (2002)

  • Volume: 52, Issue: 3, page 315-330
  • ISSN: 0232-0525

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Dąbrowicz-Tlałka, Anita, and Jankowski, Tadeusz. "Quadratic convergence of monotone iterations of differential-algebraic equations." Mathematica Slovaca 52.3 (2002): 315-330. <http://eudml.org/doc/34557>.

@article{Dąbrowicz2002,
author = {Dąbrowicz-Tlałka, Anita, Jankowski, Tadeusz},
journal = {Mathematica Slovaca},
keywords = {quasilinearization method; differential-algebraic equations; lower and upper solutions; quadratic convergence},
language = {eng},
number = {3},
pages = {315-330},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Quadratic convergence of monotone iterations of differential-algebraic equations},
url = {http://eudml.org/doc/34557},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Dąbrowicz-Tlałka, Anita
AU - Jankowski, Tadeusz
TI - Quadratic convergence of monotone iterations of differential-algebraic equations
JO - Mathematica Slovaca
PY - 2002
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 52
IS - 3
SP - 315
EP - 330
LA - eng
KW - quasilinearization method; differential-algebraic equations; lower and upper solutions; quadratic convergence
UR - http://eudml.org/doc/34557
ER -

References

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  1. BAHI J. GRIEPENTROG E.-MIELLOU J. C., Parallel treatment of a class of differential-algebraic systems, SIAM J. Numer. Anal. 33 (1996), 1969-1980. (1996) MR1411858
  2. CODDINGTON E. A.-LEVINSON N., Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955. (1955) Zbl0064.33002MR0069338
  3. DABROWICZ-TLALKA A.-JANKOWSKI T., On a differential-algebraic problem, Appl. Math. 45 (2000), 205-215. Zbl1058.34005MR1757241
  4. JACKIEWICZ Z.-KWAPISZ M., Convergence of waveform relaxation methods for differential-algebraic systems, SIAM J. Numer. Anal. 33 (1996), 2303-2317. (1996) Zbl0889.34064MR1427465
  5. JANKOWSKI T.-LAKSHMIKANTHAM V., Monotone iterations for differential equations with a parameter, J. Appl. Math. Stochastic Anal. 10 (1997), 273-278. (1997) Zbl0992.34010MR1468122
  6. JANKOWSKI T.-KWAPISZ M., Convergence of numerical methods for szstems of neutral functional-differential-algebraic equations, Appl. Math. 40 (1995), 457-472. (1995) MR1353973
  7. KWAPISZ M., On solving systems of differential algebraic equations, Appl. Math. 37 (1992), 257-264. (1992) Zbl0764.65038MR1180604
  8. LADDE G. S.-LAKSHMIKANTHAM V.-VATSALA A. S., Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman, Boston, 1985. (1985) Zbl0658.35003MR0855240
  9. LAKSHMIKANTHAM V.-VATSALA A. S., Generalized Quasilinearizatior for Nonlinear Problems, Kluwer Academic Publishers, Derdrecht, 1998. (1998) MR1640601

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