Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

A HIGHER ORDER MONOTONE ITERATIVE SCHEME FOR NONLINEAR NEUMANN BOUNDARY VALUE PROBLEMS

  • AHMAD, BASHIR (Department of Mathematics, Faculty of Science, King Abdul Aziz University) ;
  • NAZ, UZMA (Department of Mathematics, Quaid-I-Azam University) ;
  • KHAN, RAHMAT A. (Department of Mathematics, Quaid-I-Azam University)
  • Published : 2005.02.01
Download PDF
⟨ Previous Next ⟩

Abstract

The generalized quasilinearization technique has been employed to obtain a sequence of approximate solutions converging monotonically and rapidly to a solution of the nonlinear Neumann boundary value problem.

Keywords

References

  1. Bashir Ahmad, J. J. Nieto, and N. Shahzad, The Bellman Kalaba Lakshmikantham quasilinearization method for Neumann problems, J. Math. Anal. Appl. 257 (2001), 356-363 https://doi.org/10.1006/jmaa.2000.7352
  2. Bashir Ahmad, Rahmat A. Khan, and S. Sivasundaram, Generalized quasilinearization method for nonlinear boundary value problems, Dynam. Systems Appl. II, 3 (2002), 359-370
  3. Albert Cabada, J. J. Nieto, and Rafael Pita-da-veige, A note on rapid convergence of approximate solutions for an ordinary Dirichlet problem, Dyn. Contino Discrete Impuls. Syst. 4 (1998), 23-30
  4. V. Lakshmikantham, An extension of the method of quasilinearization, J. Optim, Theory Appl. 82 (1994), 315-321 https://doi.org/10.1007/BF02191856
  5. V. Lakshmikantham, Further improvement of generalized quasilinearization, Nonlinear Anal. 27 (1996), 315-321
  6. V. Lakshmikantham, S. Leela, and F. A. McRae, Improved generalized quasilinearization method, Nonlinear Anal. 24 (1995), 1627-1637 https://doi.org/10.1016/0362-546X(94)E0090-4
  7. V. Lakshmikantham and N. Shahzad, Further generalization of generalized quasilinearization method, J. Appl, Math. Stochastic Anal. 7 (1994), 545-552 https://doi.org/10.1155/S1048953394000420
  8. V. Lakshmikantham, N. Shahzad, and J. J. Nieto, Method of generalized quasilinearization for periodic boundary value problems, Nonlinear Anal. 27 (1996), 143-151 https://doi.org/10.1016/0362-546X(95)00021-M
  9. V. Lakshmikantham and A. S. Vatsala, Generalized quasilinearization for Nonlinear Problems, Kluwer Academic Publishers, Dordrecht, 1998
  10. J. J. Neito, Generalized quasilinearization method for a second order ordinary differential equation with Dirichlet boundary conditions, Proc. Amer. Math. Soc. 125 (1997), 2599-2604
  11. J. J. Neito and A. Cabada, A generalized upper and lower solutiuons method for nonlinear second order ordinary differential equations, J. Appl. Math. Stochastic Anal. 5 (1992), 157-166 https://doi.org/10.1155/S1048953392000133

Cited by

  1. Non-Monotone Convergence Schemes vol.17, pp.4, 2012, https://doi.org/10.3846/13926292.2012.711780