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

    Authors

    R. N. Mohapatra; K. Vajravelu;Y. Yin

    Comments

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    Abbreviated Journal Title

    J. Optim. Theory Appl.

    Keywords

    existence; periodic boundary-value problems; upper and lower solutions; convergence; quasilinearization; Operations Research & Management Science; Mathematics, Applied

    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.

    Journal Title

    Journal of Optimization Theory and Applications

    Volume

    99

    Issue/Number

    2

    Publication Date

    1-1-1998

    Document Type

    Article

    Language

    English

    First Page

    465

    Last Page

    480

    WOS Identifier

    WOS:000077068600009

    ISSN

    0022-3239

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