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

Author

Listed:
  • R. N. Mohapatra

    (University of Central Florida)

  • K. Vajravelu

    (University of Central Florida)

  • Y. Yin

    (Florida Institute of Technology)

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.

Suggested Citation

  • R. N. Mohapatra & K. Vajravelu & Y. Yin, 1998. "Cubic and Quartic Convergence for First-Order Periodic Boundary-Value Problems," Journal of Optimization Theory and Applications, Springer, vol. 99(2), pages 465-480, November.
    • Handle: RePEc:spr:joptap:v:99:y:1998:i:2:d:10.1023_a:1021782529131
    DOI: 10.1023/A:1021782529131
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    References listed on IDEAS

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    1. R. N. Mohapatra & K. Vajravelu & Y. Yin, 1998. "Extension of the Method of Quasilinearization and Rapid Convergence," Journal of Optimization Theory and Applications, Springer, vol. 96(3), pages 667-682, March.
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