Generalized quasilinearization method for nonlinear functional differential equations

Journal of Applied Mathematics and Stochastic Analysis

Volumn 16, Issue 1, 2003, Pages 33-43

  Ahmad, Bashir ^a   Khan, Rehmat Ali ^a   Sivasundaram, S ^b  

^a QUAID I AZAM UNIVERSITY   (Pakistan)

^b EMBRY RIDDLE AERONAUTICAL UNIVERSITY   (United States)

Author keywords

Functional Differential Equations; Generalized Quasilinearization; Quadratic convergence

Indexed keywords

EID: 13444288680     PISSN: 10489533     EISSN: 16872177     Source Type: Journal    
DOI: 10.1155/S1048953303000030     Document Type: Article

References (12)

1. Bellman, R. and Kalaba, R., Quasilinearization and Nonlinear Boundary Value Problems, American Elsevier, New York 1965.
2. Lakshmikantham, V., An extension of the method of quasilinearization, J. Optim. Theory Appl. 82(1994), 315-321.
3. Lakshmikantham, V., Further improvement of generalized quasilinearization, Nonlinear Analysis 27 (1996), 315-321.
4. Lakshmikantham, V. and Leela, S., Differential and Integral Inequalities Vol. I & II, Academic Press 1969.
5. Lakshmikantham, V., Leela, S., and McRae, F.A., Improved generalized quasilinearization method, Nonlinear Analysis 24 (1995), 1627-1637.
6. Lakshmikantham, V. and Shahzad, N., Further generalization of generalized quasilinearization method, J. Appl. Math. Stoch. Anal. 7 (1994), 545-552.
7. Lakshmikantham, V., Shahzad, N., and Nieto, J.J., Method of generalized quasilinearization for periodic boundary value problems, Nonlinear Analysis 27 (1996), 143-151.
8. Lakshmikantham, V. and Vatsala, A.S., Generalized Quasilinearization for Nonlinear Problems, Kluwer Academic Publishers, Boston 1998.
9. Nieto, J.J., Generalized quasilinearization method for a second order ordinary differential equation with Dirichlet boundary conditions, Proc. Amer. Math. Soc. 125 (1997), 2599-2604.
10. Shahzad, N. and Sivasundaram, S., Extended quasilinearization method for boundary value problems, Nonlinear World 2 (1995), 311-319.
11. Shahzad, N. and Vatsala, A.S., An extension of the Method of generalized quasilinearization for second order boundary value problems, Applicable Analysis 58 (1995), 77-83.
12. Shahzad, N. and Vatsala, A.S., Improved generalized quasilinearization for second order boundary value problems, Dynam. Systems Appl. 4 (1995), 79-85.