Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Approximating Coupled Solutions of Coupled PBVPs of Non-linear First Order Ordinary Differential Equations

  • Received : 2015.05.16
  • Accepted : 2015.11.03
  • Published : 2016.03.23
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Abstract

The present paper proposes a new monotone iteration method for existence as well as approximation of the coupled solutions for a coupled periodic boundary value problem of first order ordinary nonlinear differential equations. A new hybrid coupled fixed point theorem involving the Dhage iteration principle is proved in a partially ordered normed linear space and applied to the coupled periodic boundary value problems for proving the main existence and approximation results of this paper. An algorithm for the coupled solutions is developed and it is shown that the sequences of successive approximations defined in a certain way converge monotonically to the coupled solutions of the related differential equations under some suitable mixed hybrid conditions. A numerical example is also indicated to illustrate the abstract theory developed in the paper.

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References

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Cited by

  1. Coupled hybrid fixed point theory in a partially ordered metric space and attractivity of nonlinear hybrid fractional integral equations 2017, https://doi.org/10.1007/s11784-017-0443-z
  2. Coupled hybrid fixed point theory involving the sum and product of three coupled operators in a partially ordered Banach algebra with applications 2017, https://doi.org/10.1007/s11784-017-0471-8