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Convergence of Antiperiodic Boundary Value Problems for First-Order Integro-Differential Equations

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  • Yameng Wang
  • Juan Zhang
  • Yufeng Sun

Abstract

In this paper, we investigate the convergence of approximate solutions for a class of first-order integro-differential equations with antiperiodic boundary value conditions. By introducing the definitions of the coupled lower and upper solutions which are different from the former ones and establishing some new comparison principles, the results of the existence and uniqueness of solutions of the problem are given. Finally, we obtain the uniform and rapid convergence of the iterative sequences of approximate solutions via the coupled lower and upper solutions and quasilinearization method. In addition, an example is given to illustrate the feasibility of the method.

Suggested Citation

  • Yameng Wang & Juan Zhang & Yufeng Sun, 2020. "Convergence of Antiperiodic Boundary Value Problems for First-Order Integro-Differential Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-9, July.
    • Handle: RePEc:hin:jnddns:7254254
    DOI: 10.1155/2020/7254254
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