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Iterative Techniques for Nonlinear Periodic Boundary Value Problems (PBVPs) via Initial Value Problems

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Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 117))

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Abstract

We develop constructive methods for solving periodic boundary value problems (PBVPs) associated with a nonlinear first order scalar differential equation in a unified setting. The method of generalized quasilinearization which we employ yields rapid convergence of monotone iterates to the solution of the PBVP. The monotone iterates in our approach are solutions of linear initial value problems (IVPs) as opposed to the linear PBVPs which appear in conventional methods. We provide graphical and numerical illustrations of our results.

Dedication

The authors dedicate this chapter to the memory of the late Professor V. Lakshmikantham.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, Winston-Salem State University, Winston-Salem, NC, 27110, USA

    David H. Dezern & Sudhakar G. Pandit

Authors
  1. David H. Dezern
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  2. Sudhakar G. Pandit
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Corresponding author

Correspondence to David H. Dezern .

Editor information

Editors and Affiliations

  1. Department of Mathematics & Statistics, University of Guelph, Guelph, Ontario, Canada

    Monica G. Cojocaru

  2. Dept of Physics and Computer Science, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Ilias S. Kotsireas

  3. Department of Mathematics and MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Roman N. Makarov

  4. Department of Mathematics & MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Roderick V. N. Melnik

  5. MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Hasan Shodiev

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Dezern, D., Pandit, S. (2015). Iterative Techniques for Nonlinear Periodic Boundary Value Problems (PBVPs) via Initial Value Problems. In: Cojocaru, M., Kotsireas, I., Makarov, R., Melnik, R., Shodiev, H. (eds) Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science. Springer Proceedings in Mathematics & Statistics, vol 117. Springer, Cham. https://doi.org/10.1007/978-3-319-12307-3_49

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