Functional differential equations

Tadeusz Jankowski

Czechoslovak Mathematical Journal (2002)

  • Volume: 52, Issue: 3, page 553-563
  • ISSN: 0011-4642

Abstract

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The method of quasilinearization is a well-known technique for obtaining approximate solutions of nonlinear differential equations. In this paper we apply this technique to functional differential problems. It is shown that linear iterations converge to the unique solution and this convergence is superlinear.

How to cite

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Jankowski, Tadeusz. "Functional differential equations." Czechoslovak Mathematical Journal 52.3 (2002): 553-563. <http://eudml.org/doc/30724>.

@article{Jankowski2002,
abstract = {The method of quasilinearization is a well-known technique for obtaining approximate solutions of nonlinear differential equations. In this paper we apply this technique to functional differential problems. It is shown that linear iterations converge to the unique solution and this convergence is superlinear.},
author = {Jankowski, Tadeusz},
journal = {Czechoslovak Mathematical Journal},
keywords = {quasilinearization; monotone iterations; superlinear convergence; quasilinearization; monotone iterations; superlinear convergence},
language = {eng},
number = {3},
pages = {553-563},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Functional differential equations},
url = {http://eudml.org/doc/30724},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Jankowski, Tadeusz
TI - Functional differential equations
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 3
SP - 553
EP - 563
AB - The method of quasilinearization is a well-known technique for obtaining approximate solutions of nonlinear differential equations. In this paper we apply this technique to functional differential problems. It is shown that linear iterations converge to the unique solution and this convergence is superlinear.
LA - eng
KW - quasilinearization; monotone iterations; superlinear convergence; quasilinearization; monotone iterations; superlinear convergence
UR - http://eudml.org/doc/30724
ER -

References

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  1. Methods of Nonlinear Analysis, Vol. I, Academic Press, New York, 1973. (1973) MR0381408
  2. Quasilinearization and Nonlinear Boundary Value Problems, American Elsevier, New York, 1965. (1965) MR0178571
  3. Introduction to Functional Differential Equations, Springer-Verlag, New York, Berlin, 1993. (1993) MR1243878
  4. An extension of the method of quasilinearization for differential problems with a parameter, Nonlinear Stud. 6 (1999), 21–44. (1999) MR1691903
  5. Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman, Boston, 1985. (1985) MR0855240
  6. 10.1007/BF02192570, J.  Optim. Theory Appl. 87 (1995), 379–401. (1995) MR1358749DOI10.1007/BF02192570
  7. Generalized Quasilinearization for Nonlinear Problems, Kluwer Academic Publishers, Dordrecht-Boston-London, 1998. (1998) MR1640601

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