Extension of the Method of Quasilinearization and Rapid Convergence

被引:0
作者
R. N. Mohapatra
K. Vajravelu
Y. Yin
机构
[1] University of Central Florida,Department of Mathematics
[2] Florida Institute of Technology,Department of Applied Mathematics
来源
Journal of Optimization Theory and Applications | 1998年 / 96卷
关键词
Existence; nonlinear initial-value problems; upper and lower solutions; convergence; quasilinearization;
D O I
暂无
中图分类号
学科分类号
摘要
An extension of the method of quasilinearization has been applied to first-order nonlinear initial-value problems (IVP for short). It has been shown that there exist monotone sequences which converge rapidly to the unique solution of IVP.
引用
收藏
页码:667 / 682
页数:15
相关论文
共 13 条
[1]  
Bellman R.(1955)Functional Equations in the Theory of Dynamic Programming, II: Nonlinear Differential Equations Proceedings of the National Academy of Sciences 41 481-483
[2]  
Bellman R.(1955)Functional Equations in the Theory of Dynamic Programming, V: Positivity and Quasilinearity Proceedings of the National Academy of Sciences 41 743-746
[3]  
Kalaba R.(1959)On Nonlinear Differential Equations, the Maximum Operation, and Monotone Convergence Journal of Mathematics and Mechanics 8 519-574
[4]  
Lakshmikantham V.(1996)Further Improvement of Generalized Quasilinearization Method Nonlinear Analysis 27 223-227
[5]  
Lakshmikantham V.(1994)Another Extension of the Method of Quasilinearization Journal of Mathematical Analysis and Applications 185 545-569
[6]  
Koksal S.(1995)Improved Quasilinearization (GQL) Method Nonlinear Analysis 24 1627-1637
[7]  
Lakshmikantham V.(1995)Generalized Quasilinearization for Nonlinear First-Order Ordinary Differential Equations Nonlinear Times and Digest 2 1-9
[8]  
Leela S.(1994)Further Generalization of Generalized Quasilinearization Method Journal of Applied Mathematics and Stochastic Analysis 7 545-552
[9]  
McRae F. A.(undefined)undefined undefined undefined undefined-undefined
[10]  
Lakshmikantham V.(undefined)undefined undefined undefined undefined-undefined