The quasilinearization method on an unbounded domain

Proceedings of the American Mathematical Society

Volumn 131, Issue 5, 2003, Pages 1481-1488

  Eloe, Paul W ^a  

^a UNIVERSITY OF DAYTON   (United States)

Author keywords

Quadratic convergence; Quasilinearization; Singular boundary value problems; Upper and lower solutions

Indexed keywords

EID: 0037407026     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-02-06654-6     Document Type: Conference Paper

References (15)

1. J. W. Bebernes and L. K. Jackson, Infinite interval boundary value problems for y″ = f(t, y), Duke Math. J., 34 (1967), 39-47. MR 34:6205
2. R. Bellman, Methods of Nonlinear Analysis, Vol. II Academic Press, New York, 1973. MR 52:2305
3. R. Bellman and R. Kalaba, Quasilinearization and Nonlinear Boundary Value Problems, Elsevier, New York, 1965. MR 31:2828
4. A. Cabada, J. Nieto and R. Pita-da-Viega, A note on rapid convergence of approximate solutions for an ordinary Dirichlet problem, Dynam. Contin. Discrete Impuls. Systems, 4 (1998), 23-30. MR 98k:34020
5. J. V. Devi and A. S. Vatsala, Quasilinearization for second order singular boundary value problems with solutions in weighted spaces, J. Korean Math. Soc., 37 (2000), 823-833.
6. V. Doddaballapur and P. W. Eloe, Monotone and quadratic convergence of approximate solutions of ordinary differential equations with impulse, Comm. Appl. Analysis, 2 (1998), 373-382. MR 99d:34021
7. V. Doddaballapur, P. W. Eloe and Y. Zhang, Quadratic convergence of approximate solutions of two-point boundary value problems with impulse, Electronic J. Differential Equations, Conf. 01, (1997), 81-95. MR 99m:34019
8. P. W. Eloe, L. J. Grimm and J. Mashburn, A boundary value problem on an unbounded domain, Differential Equations and Dynamical Systems, 8 (2000), 125-140.
9. P. W. Eloe and S. G. Hristova, Application of the method of quasilinearization for the initial value problem for systems of impulsive differential equations, preprint.
10. P. W. Eloe and Y. Zhang, A quadratic monotone iteration scheme for two-point boundary value problems for ordinary differential equations, Nonlinear Analysis, 33 (1998), 443-453. MR 99e:34015
11. V. Lakschmikantham, S. Leela, and F. A. McRae, Improved generalized quasilinearization (GQL) method, Nonlinear Analysis, 24 (1995), 1627-1637. MR 96a:34023
12. V. Lakschmikantham and A. S. Vatsala, Generalized Quasilinearization for Nonlinear Problems, Kluwer Academic Publishers, Dordrecht, 1998. MR 99k:34013
13. R. N. Mohapatra, K. Vajravelu and Y. Yin, Generalized quasilinearization method for second order boundary value problem, Nonlinear Analysis, 36 (1999), 799-806. MR 2000f:34038
14. J. Nieto, Generalized quasilinearization method for a second order differential equation with Dirichlet boundary conditions, Proc. Amer. Math. Soc., 125 (1997), 2599-2604. MR 97j:34015
15. N. Shahzad and A. S. Vatsala, An extension of the method of generalized quasilinearization for second order boundary value problems, Applicable Analysis, 58 (1995), 77-83. MR 97a:34063