Spectral approximated superconvergent methods for system of nonlinear Volterra Hammerstein integral equations

Samiran Chakraborty, Shivam Kumar Agrawal and Gnaneshwar Nelakanti

Chaos, Solitons & Fractals, 2025, vol. 192, issue C

Abstract: In this article, we develop the Jacobi spectral multi-Galerkin method alongside the Kumar-Sloan technique to approximate systems of non-linear Volterra Hammerstein integral equations. We conduct a comprehensive superconvergence analysis for both smooth and weakly singular kernels in both infinity and weighted-L2 norms. Our findings include the derivation of superconvergence rates for the multi-Galerkin method without resorting to iterated versions. Notably, our conclusions highlight the enhanced performance of multi-Galerkin approximation compared to Jacobi spectral Galerkin methods, while maintaining the same system size for both Jacobi spectral multi-Galerkin and Galerkin methods. To validate the robustness and efficiency of our theoretical results, numerical examples are provided.

Keywords: System of Volterra–Hammerstein integral equations; Spectral multi-Galerkin method; Superconvergence; Smooth kernels; Weakly singular kernels; Jacobi polynomials (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077925000219
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:192:y:2025:i:c:s0960077925000219

DOI: 10.1016/j.chaos.2025.116008

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().