Cubic and quartic convergence for first-order periodic boundary-value problems

被引：0

作者：

Mohapatra, RN ^{[1
]}

Vajravelu, K

Yin, Y

机构：

[1] Univ Cent Florida, Dept Math, Orlando, FL 32816 USA

[2] Florida Inst Technol, Dept Appl Math, Melbourne, FL 32901 USA

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 1998年 / 99卷 / 02期

关键词：

existence; periodic boundary-value problems; upper and lower solutions; convergence; quasilinearization;

D O I：

10.1023/A:1021782529131

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper, the results of Lakshmikantham et al. (Ref. 1) for first-order periodic boundary-value problems are extended, by using the extended method of quaislinearization and rapid convergence for initial-value problems of Mohapatra et al. (Ref 2). Also, it is shown that monotone sequences converge cubically to the unique solution when the forcing function in the differential equation is 2-hyperconvex and converge quartically when the forcing function is 3-hyperconvex. Several other generalizations of the problem are also presented.

引用

页码：465 / 480

页数：16

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