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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2024. Vol 50

Fuzzy Volterra Integral Equations with Piecewise Continuous Kernels: Theory and Numerical Solution

Author(s)
Samad Noeiaghdam1,2, Denis N. Sidorov2,3,4, Aliona I. Dreglea2,3

1Institute of Mathematics, Henan Academy of Sciences, Zhengzhou, China

2Irkutsk National Research Technical University, Irkutsk, Russian Federation Российская Федерация

3Harbin Institute of Technology, Harbin, China

4Melentiev Energy Systems Institute SB RAS, Irkutsk, Russian Federation

Abstract
This research focuses on addressing both linear and nonlinear fuzzy Volterra integral equations that feature piecewise continuous kernels. The problem is tackled using the method of successive approximations. The study discusses the existence and uniqueness of solutions for these fuzzy Volterra integral equations with piecewise kernels. Numerical results are obtained by applying the successive approximations method to examples for both linear and nonlinear scenarios. Error analysis graphs are plotted to illustrate the accuracy of the method. Furthermore, a comparative analysis is presented through graphs of approximate solutions for different fuzzy parameter values. To highlight the effectiveness and significance of the successive approximations method, a comparison is made with the traditional homotopy analysis technique. The results indicate that the successive approximation method outperforms the homotopy analysis method in terms of accuracy and effectiveness.
About the Authors

Samad Noeiaghdam, PhD of Applied Mathematics, Assoc. Prof., Institute of Mathematics, Henan Academy of Sciences, Zhengzhou, 450046, China, Irkutsk National Research Technical University, Irkutsk, 664074, Russia, snoei@hnas.ac.cn; snoei@istu.edu

Denis N. Sidorov, Dr. Sci. (Phys.–Math.), Prof., Irkutsk National Research Technical University, Irkutsk, 664074, Russian Federation; Harbin Institute of Technology, Harbin, 150001, China; Melentiev Energy Systems Institute SB RAS, Irkutsk, 664033, Russia, dsidorov@isem.irk.ru

Aliona I. Dreglea, Cand. Sci. (Phys.-Math.), Assoc. Prof., Irkutsk National Research Technical University, Irkutsk, 664074, Russian Federation; Harbin Institute of Technology, Harbin, 150001, China, adreglea@istu.edu

For citation

Noeiaghdam S., Sidorov D. N., Dreglea A. I. Fuzzy Volterra Integral Equations with Piecewise Continuous Kernels: Theory and Numerical Solution. The Bulletin of Irkutsk State University. Series Mathematics, 2024, vol. 50, pp. 36–50.

https://doi.org/10.26516/1997-7670.2024.50.36

Keywords
fuzzy Volterra integral equation, piecewise kernel, successive approximation, error estimation
UDC
519.64, 510.644.4
MSC
45D05, 65R20, 45G10
DOI
https://doi.org/10.26516/1997-7670.2024.50.36
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