Theoretical and numerical aspects for the second kind of generalized nonlinear Volterra-Fredholm integral equations
*Ahmed S. RahbyCorresponding authora.s.rahby@fsc.bu.edu.egDepartment of MathematicsFaculty of ScienceBenha UniversityBenha, 13518, EgyptView full profile → , Mohamed A. Abdouabdella_777@yahoo.comDepartment of MathematicsFaculty of EducationAlexandria UniversityAlexandria, 21544, EgyptView full profile → , Gamal A. Mosagamal.mossoua@fsc.bu.edu.egDepartment of MathematicsFaculty of ScienceBenha UniversityBenha, 13518, EgyptView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Jun 2024
- Published Online:
- 31 Aug 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2149
- Pages:
- 1–17
Abstract
We investigate the existence and uniqueness of solutions to the second kind of generalized nonlinear Volterra-Fredholm integral equations (GNV-FIEs). These equations are analyzed using the Banach fixed point theorem and Picard’s approach, particularly in situations where Picard’s method might not work. We also present a new numerical method which incorporates quadrature principles, including Simpson’s 3/8 and Romberg, with the modified Adomian decomposition method (MADM). This method can be extremely effective when calculating definite integrals becomes challenging. We begin our paper with a brief overview of the topic and then go into great detail into the suggested approach. We then illustrate the applicability of the theoretical results through numerical examples, which are presented in tables and figures for clarity.
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References
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