Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Generalized quasilinearization method
for a second order ordinary differential
equation with Dirichlet boundary conditions

Author: Juan J. Nieto
Journal: Proc. Amer. Math. Soc. 125 (1997), 2599-2604
MSC (1991): Primary 34A45, 34B15
MathSciNet review: 1402880
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study the existence and approximation of solutions for a nonlinear second order ordinary differential equation with Dirichlet boundary value conditions. We present a generalized quasilinearization technique to obtain a sequence of approximate solutions converging quadratically to a solution.

References [Enhancements On Off] (What's this?)

  • 1. R. Bellman, Methods of Nonlinear Analysis, Vol. II. Academic Press, New York, 1973.
  • 2. R. Bellman and R. Kalaba, Quasilinearization and Nonlinear Boundary Value Problems. American Elsevier, New York, 1965. MR 31:2828
  • 3. G. S. Ladde, V. Lakshmikantham and A. S. Vatsala, Monotone Iterative Techniques for Nonlinear Differential Equations. Pitman, Boston, 1985. MR 88g:35006
  • 4. V. Lakshmikantham, An Extension of the Method of Quasilinearization. J. Optimization Theory Appl. 82 (1994), 315-321. MR 95d:34021
  • 5. V. Lakshmikantham and S. Malek, Generalized Quasilinearization. Nonlinear World 1 (1994), 59-63. MR 95d:34020
  • 6. V. Lakshmikantham and J. J. Nieto, Generalized Quasilinearization for Nonlinear First Order Differential Equations. Nonlinear Times and Digest 2 (1995), 1-10. MR 96c:34025
  • 7. V. Lakshmikantham, N. Shahzad and J. J. Nieto, Methods of Generalized Quasilinearization for Periodic Boundary Value Problems, Nonlinear Anal. 27 (1996), 143-151. CMP 96:12
  • 8. J. J. Nieto and A. Cabada, A Generalized Upper and Lower Solution Method for Nonlinear Second Order Ordinary Differential Equations. J. Applied Math. Stochastic Anal. 5 (1992), 157-166. MR 94c:34033
  • 9. N. Shahzad and S. Sivasundaram, Further Generalization of Quasilinearization Method for Boundary Value Problems, Nonlinear Times and Digest 2 (1995), 59-68. MR 96b:34013
  • 10. N. Shahzad and A. S. Vatsala, Improved Generalized Quasilinearization Method for Second Order Boundary Value Problems. Dynam. Systems Appl. 4 (1995), 79-85. MR 95i:34018

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 34A45, 34B15

Retrieve articles in all journals with MSC (1991): 34A45, 34B15

Additional Information

Juan J. Nieto
Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, Spain

Keywords: Dirichlet problem, generalized quasilinearization, quadratic convergence
Received by editor(s): March 13, 1996
Additional Notes: The author’s research was partially supported by D.G.I.C.Y.T. (Spain), project PB94-0610, and by EC Network, CHRX-CT94-0555
Communicated by: Hal L. Smith
Article copyright: © Copyright 1997 American Mathematical Society