An extension of the method of quasilinearization

Tadeusz Jankowski

Archivum Mathematicum (2003)

  • Volume: 039, Issue: 3, page 201-208
  • ISSN: 0044-8753

Abstract

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The method of quasilinearization is a well–known technique for obtaining approximate solutions of nonlinear differential equations. This method has recently been generalized and extended using less restrictive assumptions so as to apply to a larger class of differential equations. In this paper, we use this technique to nonlinear differential problems.

How to cite

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Jankowski, Tadeusz. "An extension of the method of quasilinearization." Archivum Mathematicum 039.3 (2003): 201-208. <http://eudml.org/doc/249143>.

@article{Jankowski2003,
abstract = {The method of quasilinearization is a well–known technique for obtaining approximate solutions of nonlinear differential equations. This method has recently been generalized and extended using less restrictive assumptions so as to apply to a larger class of differential equations. In this paper, we use this technique to nonlinear differential problems.},
author = {Jankowski, Tadeusz},
journal = {Archivum Mathematicum},
keywords = {quasilinearization; monotone iterations; quadratic convergence; monotone iterations; quadratic convergence},
language = {eng},
number = {3},
pages = {201-208},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {An extension of the method of quasilinearization},
url = {http://eudml.org/doc/249143},
volume = {039},
year = {2003},
}

TY - JOUR
AU - Jankowski, Tadeusz
TI - An extension of the method of quasilinearization
JO - Archivum Mathematicum
PY - 2003
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 039
IS - 3
SP - 201
EP - 208
AB - The method of quasilinearization is a well–known technique for obtaining approximate solutions of nonlinear differential equations. This method has recently been generalized and extended using less restrictive assumptions so as to apply to a larger class of differential equations. In this paper, we use this technique to nonlinear differential problems.
LA - eng
KW - quasilinearization; monotone iterations; quadratic convergence; monotone iterations; quadratic convergence
UR - http://eudml.org/doc/249143
ER -

References

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  2. Quasilinearization and Nonlinear Boundary Value Problems, American Elsevier, New York 1965. MR0178571
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  4. An extension of the method of quasilinearization for differential problems with a parameter, Nonlinear Stud. 6 (1999), 21–44. MR1691903
  5. Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman 1985. MR0855240
  6. Generalized quasilenearization, Nonlinear World 1 (1994), 59–63. MR1282859
  7. Extensions of the Method of Quasilinearization, J. Optimization Theory Appl. Vol. 87 (1995), 379–401. MR1358749
  8. Generalized Quasilinearization for Nonlinear Problems, Kluwer Academic Publishers, Dordrecht 1998. MR1640601
  9. Improved Generalized Quasilinearization Method, Nonlinear Analysis 24 (1995), 1627–1637. MR1328588
  10. Further Generalization of Generalized Quasilinearization Method, J. Appl. Math. Stoch. Anal. 7 (1994), 545–552. MR1310927
  11. An Extension of the Method of Generalized Quasilinearization for Second Order Boundary Value Problems, Appl. Anal. 58 (1995), 77–83. MR1384590

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