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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-article-PWA5-0018-0009

Czasopismo

Demonstratio Mathematica

Tytuł artykułu

Extended method of quasilinearization for a nonlinear three-point boundary value problem

Autorzy Ahmad, B.  Alsaedi, A.  Garout, D. 
Treść / Zawartość https://www.degruyter.com/view/j/dema
Warianty tytułu
Języki publikacji EN
Abstrakty
EN In this paper, we discuss the generalized quasilinearization technique for a second order nonlinear differential equation with nonlinear three-point general boundary conditions. In fact, we obtain sequences of upper and lower solutions converging mono- tonically and quadratically to the unique solution of the nonlinear three-point boundary value problem.
Słowa kluczowe
PL zagadnienie brzegowe   zbieżność kwadratowa   brzeg ustalony   metoda rozszerzona  
EN boundary value problem   quadratic convergence   certain boundary   extended method  
Wydawca De Gruyter
Czasopismo Demonstratio Mathematica
Rocznik 2006
Tom Vol. 39, nr 4
Strony 803--814
Opis fizyczny Bibliogr. 16 poz.
Twórcy
autor Ahmad, B.
autor Alsaedi, A.
autor Garout, D.
  • Department of Mathematics Faculty of Science King Abdul Aziz University P.O. Box 80257 Jeddah 21589, Saudi Arabia, bashir_qua@yahoo.com
Bibliografia
[1] R. Bellman and R. Kalaba, Quasilinearization and Nonlinear Boundary Value Problems, Amer. Elsevier, New York, 1965.
[2] V. Lakshmikantham, An extension of the method of quasilinearization, J. Optim. Theory Appl. 82 (1994), 315–321.
[3] V. Lakshmikantham, Further improvement of generalized quasilinearization, Nonlinear Anal. 27 (1996), 223–227.
[4] V. Lakshmikantham and A. S. Vatsala, Generalized Quasilinearization for Nonlinear Problems, Kluwer Academic Publishes, Dordrecht, 1998.
[5] J. J. Nieto, Generalized quasilinearization method for a second order differential equation with Dirichlet boundary conditions, Proc. Amer. Math. Soc. 125 (1997), 2599–2604.
[6] A. Cabada, J. J. Nieto and R. Pita-da-Veige, A note on rapid convergence of approximate solutions for an ordinary Dirichlet problem, Dynam. Contin. Discrete Impuls. Systems 4 (1998), 23–30.
[7] A. Cabada and J. J. Nieto, Quasilinearization and rate of convergence for higher order nonlinear periodic boundary value problems, J. Optim. Theory Appl. 108 (2001), 97–107.
[8] B. Ahmad, J. J. Nieto and N. Shahzad, The Bellman-Kalaba-Lakshmikantham quasilinearization method for Neumann problems, J. Math. Anal. Appl. 257 (2001), 356–363.
[9] B. Ahmad, J. J. Nieto and N. Shahzad, Generalized quasilinearization method for mixed boundary value problems, App. Math. Comput. 133 (2002), 423–429.
[10] B. Ahmad, A. Alsaedi and S. Sivasundaram, Approximation of the solution of nonlinear second order integro-differential equations, Dynamic Systems Appl. (to appear).
[11] W. Coppel, Disconjugacy, Lecture Notes in Mathematics, Vol. 220, Springer-Verlag, NewYork/Berlin, 1971.
[12] I. T. Kiguradze and A. G. Lomtatidze, On certain boundary value problems for second order linear ordinary differential equations with singularities, J. Math. Anal. Appl. 101 (1984), 325–347.
[13] C. P. Gupta, A second order m-point boundary value problem at resonance, Nonlinear Anal. 24 (1995), 1483–1489.
[14] C. P. Gupta and S. Trofimchuck, A priori estimates for the existence of a solution for a multi-point boundary value problem, J. Inequal. Appl. 5 (2000), 351–365.
[15] P. Eloe and Y. Gao, The method of quasilinearization and a three-point boundary value problem, J. Korean Math. Soc. 39 (2002) 319–330.
[16] B. Ahmad and T. G. Sogati, A second order three-point boundary value problem with mixed nonlinear boundary conditions, Methods Appl. Anal. 11 (2004), 295–302.
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