Algorithm for Equations of Hammerstein Type and Applications

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  • Mathew Aibinu1,
  • Surendra C. Thakur2,
  • Sibusiso Moyo3,
  1. Institute for Systems Science & KZN e-Skills CoLab, Durban University of Technology, Durban 4000, South Africa DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), Johannesburg, South Africa National Institute for Theoretical and Computational Sciences (NITheCS), South Africa
  2. KZN e-Skills CoLab, Durban University of Technology, Durban 4000, South Africa.
  3. Institute for Systems Science & Office of the DVC Research, Innovation & Engagement, Milena Court, Durban University of Technology, Durban 4000, South Africa.

Published in Issue 2025-11-09

How to Cite

Algorithm for Equations of Hammerstein Type and Applications. (2025). Communications in Nonlinear Analysis, 11(1). https://oiccpress.com/cna/article/view/17850

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Abstract

Equations of Hammerstein type cover large variety of areas and are of much interest to a wide audience due to the fact that they have applications in numerous areas. Suitable conditions are imposed to obtain a strong convergence result for nonlinear integral equations of Hammerstein type with monotone type mappings. A technique which does not involve the assumption of existence of a real constant whose calculation is unclear has been used in this study to obtain the strong convergence result. Moreover, our technique is applied to show the forced oscillations of finite amplitude of a pendulum as a specific example of nonlinear integral equations of Hammerstein type. Numerical example is given for the illustration of the convergence of the sequences of iteration. These are done to demonstrate to our readers that this approach can be applied to problems arising in physical systems.

Keywords

  • Hammerstein equation,
  • monotone type mapping,
  • strong convergence,
  • forced oscillations,
  • finite amplitude of a pendulum
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