On a differential-algebraic problem

Anita Dąbrowicz-Tlałka; Tadeusz Jankowski

Applications of Mathematics (2000)

  • Volume: 45, Issue: 3, page 205-215
  • ISSN: 0862-7940

Abstract

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The method of quasilinearization is a procedure for obtaining approximate solutions of differential equations. In this paper, this technique is applied to a differential-algebraic problem. Under some natural assumptions, monotone sequences converge quadratically to a unique solution of our problem.

How to cite

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Dąbrowicz-Tlałka, Anita, and Jankowski, Tadeusz. "On a differential-algebraic problem." Applications of Mathematics 45.3 (2000): 205-215. <http://eudml.org/doc/33055>.

@article{Dąbrowicz2000,
abstract = {The method of quasilinearization is a procedure for obtaining approximate solutions of differential equations. In this paper, this technique is applied to a differential-algebraic problem. Under some natural assumptions, monotone sequences converge quadratically to a unique solution of our problem.},
author = {Dąbrowicz-Tlałka, Anita, Jankowski, Tadeusz},
journal = {Applications of Mathematics},
keywords = {differential-algebraic problem; monotone sequences; quadratic convergence; differential-algebraic problem; monotone sequences; quadratic convergence},
language = {eng},
number = {3},
pages = {205-215},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a differential-algebraic problem},
url = {http://eudml.org/doc/33055},
volume = {45},
year = {2000},
}

TY - JOUR
AU - Dąbrowicz-Tlałka, Anita
AU - Jankowski, Tadeusz
TI - On a differential-algebraic problem
JO - Applications of Mathematics
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 45
IS - 3
SP - 205
EP - 215
AB - The method of quasilinearization is a procedure for obtaining approximate solutions of differential equations. In this paper, this technique is applied to a differential-algebraic problem. Under some natural assumptions, monotone sequences converge quadratically to a unique solution of our problem.
LA - eng
KW - differential-algebraic problem; monotone sequences; quadratic convergence; differential-algebraic problem; monotone sequences; quadratic convergence
UR - http://eudml.org/doc/33055
ER -

References

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  1. 10.1137/S0036142993258105, SIAM J.  Numer. Anal. 33 (1996), 1969–1980. (1996) MR1411858DOI10.1137/S0036142993258105
  2. Quasilinearization and Nonlinear Boundary Value Problems, American Elsevier, New York, 1965. (1965) MR0178571
  3. 10.1137/S0036142992233098, SIAM J.  Numer. Anal. 33 (1996), 2303–2317. (1996) MR1427465DOI10.1137/S0036142992233098
  4. 10.1155/S1048953397000348, J. Appl. Math. Stoch. Anal. 10 (1997), 273–278. (1997) MR1468122DOI10.1155/S1048953397000348
  5. Convergence of numerical methods for systems of neutral functional-differential-algebraic eguations, Appl. Math. 40 (1995), 457–472. (1995) MR1353973
  6. On solving systems of differential algebraic eguations, Appl. Math. 37 (1992), 257–264. (1992) MR1180604
  7. Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman, Boston, 1985. (1985) MR0855240

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