Title

Cubic and Quartic Convergence for First-Order Periodic Boundary-Value Problems

Keywords

Convergence; Existence; Periodic boundary-value problems; Quasilinearization; Upper and lower solutions

Abstract

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.

Publication Date

1-1-1998

Publication Title

Journal of Optimization Theory and Applications

Volume

99

Issue

2

Number of Pages

465-480

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1023/A:1021782529131

Socpus ID

0032357426 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0032357426

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