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The proposed Newton-iteration scheme based upon iterated Galerkin operator ensures improved convergence rates at every step of iteration. Specifically, we establish that the convergence rate in iterated Galerkin method increases by O(hr) for smooth kernel, and O(h1\u2212\u03b1) for weakly singular kernel, in each step of reiteration, where h is the norm of the partition. Numerical examples are provided to justify the reliability and efficiency of the proposed technique.<\/jats:p>","DOI":"10.3846\/mma.2026.22594","type":"journal-article","created":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T14:37:46Z","timestamp":1770734266000},"page":"214-227","update-policy":"https:\/\/doi.org\/10.3846\/mma_policy","source":"Crossref","is-referenced-by-count":0,"title":["Re-iterated approximation methods for nonlinear Volterra integral equations"],"prefix":"10.3846","volume":"31","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-3128-0199","authenticated-orcid":true,"given":"Samiran","family":"Chakraborty","sequence":"first","affiliation":[{"name":"Department of Mathematics, National Institute of Technology Jamshedpur","place":["Jamshedpur, India"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6812-9167","authenticated-orcid":true,"given":"Kapil","family":"Kant","sequence":"additional","affiliation":[{"name":"Department of Engineering Sciences, ABV-Indian Institute of Information Technology and Management","place":["Gwalior, India"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-2909-1938","authenticated-orcid":true,"given":"Ritu","family":"Nigam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Kharagpur","place":["Kharagpur, India"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5247-9696","authenticated-orcid":true,"given":"Gnaneshwar","family":"Nelakanti","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Kharagpur","place":["Kharagpur, India"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2209","published-online":{"date-parts":[[2026,2,10]]},"reference":[{"key":"10.3846\/mma.2026.22594-0","doi-asserted-by":"publisher","unstructured":"M. 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