Adaptive Methods For the Solution of Nonlinear Hammerstein IntegralEquations

Authors

  • Samira Siahmansouri Department of Information Technology, Arike Perspolis Applied Scientific Education Center, Varamin, Iran.
  • Esmaeil Yousef * Department of Mathematics and Computer Science, SR.C, Islamic Azad University, Tehran, Iran.
  • Samanh Neyshabouri Department of Mathematics Qazvin Branch, Islamic Azad University, Qazvin, Iran.

https://doi.org/10.48314/jidcm.v1i3.76

Abstract

In this study, a novel approach is proposed for solving nonlinear Hammerstein integral equations. The
core of the method is based on a modified Simpson’s quadrature rule. As an extension of the classical
Simpson’s rule, the modified version aims to enhance accuracy, improve the rate of convergence, and
adapt to the complex behavior of functions. The proposed method employs an iterative procedure
combined with an adaptive refinement of the integration interval according to error estimates. This feature
focuses computational effort on sensitive parts of the function while reducing unnecessary evaluations.
Furthermore, a convergence analysis of the method is presented to ensure its theoretical validity. Several
numerical examples are also provided to demonstrate the efficiency and accuracy of the approach. The
results indicate that the proposed method yields more accurate approximations and faster convergence
compared to existing techniques, making it a valuable tool for solving complex computational problems,
such as differential equations and physical simulations.

Keywords:

Simpson’s quadrature rule, Nonlinear, Hammerstein, Integral equations, Quadrature

References

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Published

2025-09-24

Issue

Vol. 1 No. 3 (2025): Journal of Intelligent Decision and Computational Modelling (JIDCM)

Section

Articles

How to Cite

Siahmansouri, S. ., Yousef, E. ., & Neyshabouri, S. . (2025). Adaptive Methods For the Solution of Nonlinear Hammerstein IntegralEquations. Journal of Intelligent Decision and Computational Modelling, 1(3), 210-217. https://doi.org/10.48314/jidcm.v1i3.76