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

R. N. Mohapatra, K. Vajravelu and Y. Yin
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R. N. Mohapatra: University of Central Florida
K. Vajravelu: University of Central Florida
Y. Yin: Florida Institute of Technology

Journal of Optimization Theory and Applications, 1998, vol. 99, issue 2, No 9, 465-480

Abstract: 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.

Keywords: Existence; periodic boundary-value problems; upper and lower solutions; convergence; quasilinearization (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1023/A:1021782529131

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