Generalized quasilinearization method and higher order of convergence for second-order boundary value problems

Boundary Value Problems

Volumn 2006, Issue , 2006, Pages

  Melton, Tanya G ^a   Vatsala, A S ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33745350587     PISSN: 16872762     EISSN: 16872770     Source Type: Journal    
DOI: 10.1155/BVP/2006/25715     Document Type: Article

References (15)

1. R. E. Bellman Methods of Nonlinear Analysis. Vol. 1 61-I Mathematics in Science and Engineering Academic Press New York 1970
2. R. E. Bellman R. E. Kalaba Quasilinearization and Nonlinear Boundary-Value Problems Modern Analytic and Computional Methods in Science and Mathematics 3 American Elsevier New York 1965
3. S. R. Bernfeld V. Lakshmikantham An Introduction to Nonlinear Boundary Value Problems Mathematics in Science and Engineering 109 Academic Press New York 1974
4. A. Cabada J. J. Nieto Rapid convergence of the iterative technique for first order initial value problems Applied Mathematics and Computation 87 1997 2-3 217-226
5. A. Cabada J. J. Nieto Quasilinearization and rate of convergence for higher-order nonlinear periodic boundary-value problems Journal of Optimization Theory and Applications 108 2001 1 97-107
6. S. Heikkilä V. Lakshmikantham Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations Monographs and Textbooks in Pure and Applied Mathematics 181 Marcel Dekker New York 1994
7. G. S. Ladde V. Lakshmikantham A. S. Vatsala Monotone Iterative Techniques for Nonlinear Differential Equations Monographs, Advanced Texts and Surveys in Pure and Applied Mathematics 27 Pitman Massachusetts 1985
8. V. Lakshmikantham J. J. Nieto Generalized quasilinearization iterative method for initial value problems Nonlinear Studies 2 1995 1-9
9. V. Lakshmikantham A. S. Vatsala Generalized Quasilinearization for Nonlinear Problems Mathematics and Its Applications 440 Kluwer Academic Dordrecht 1998
10. V. B. Mandelzweig Quasilinearization method and its verification on exactly solvable models in quantum mechanics Journal of Mathematical Physics 40 1999 12 6266-6291
11. V. B. Mandelzweig F. Tabakin Quasilinearization approach to nonlinear problems in physics with application to nonlinear ODEs Computer Physics Communications 141 2001 2 268-281
12. T. Melton A. S. Vatsala Generalized quasilinearization and higher order of convergence for first order initial value problems to appear in Dynamic Systems Applications
13. R. N. Mohapatra K. Vajravelu Y. Yin Extension of the method of quasilinearization and rapid convergence Journal of Optimization Theory and Applications 96 1998 3 667-682
14. M. Sokol A. S. Vatsala A unified exhaustive study of monotone iterative method for initial value problems Nonlinear Studies 8 2001 4 429-438
15. I. H. West A. S. Vatsala Generalized monotone iterative method for initial value problems Applied Mathematics Letters 17 2004 11 1231-1237