A Newton–Cotes-Based Iterative Scheme for Nonlinear Fuzzy Volterra Integral Equation

Document Type : Research Paper

Authors

1 Department of Mathematics, Shahriar Branch, Islamic Azad University, Shahriar, Iran

2 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

Abstract

This paper introduces a novel iterative numerical method for solving nonlinear fuzzy Volterra integral equations using Newton–Cotes (NC) quadrature rules. The core idea is to apply auxiliary Newton–Cotes rules (ANCR) over subintervals of the domain, enabling more flexible and accurate approximations of fuzzy integrals. A detailed convergence analysis is presented to establish the method’s validity and efficiency. The scheme operates within a complete fuzzy metric space and ensures convergence under Lipschitz continuity conditions in the kernel using fixed-point theory. The results show that this method can provide a significant improvement in computational accuracy and generality compared to current methods and offers a suitable opportunity for future research in the field of nonlinear fuzzy integral equations. These results demonstrate that the ANCR scheme offers both provable convergence and practical advantage in accuracy and overall computational cost for a broad class of nonlinear fuzzy Volterra problems.

Keywords

Main Subjects

References

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Iranian Journal of Fuzzy Systems
Volume 23, Issue 1
January and February 2026
Pages 95-109

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