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Convergence and data dependence results of the nonlinear Volterra integral equation by the Picard's three step iteration

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info:eu-repo/semantics/openAccess

Date

2024

Author

Cona, Lale

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Scopus EXPORT DATE: 07 June 2024 @ARTICLE{Cona202418048, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85194225489&doi=10.3934%2fmath.2024880&partnerID=40&md5=19cd1ba986f70fc87577786476ced11d}, affiliations = {Gumushane University, Faculty of Engineering and Natural Sciences, Department of Mathematical Engineering, Gumushane, Turkey}, correspondence_address = {L. Cona; Gumushane University, Faculty of Engineering and Natural Sciences, Department of Mathematical Engineering, Gumushane, Turkey; email: lalecona@gumushane.edu.tr}, publisher = {American Institute of Mathematical Sciences}, issn = {24736988}, language = {English}, abbrev_source_title = {AIMS Math.} }

Abstract

Picard's three step iteration algorithm was one of the iteration algorithms that was recently shown to be faster than some other iterative algorithms in the existing literature. The purpose of this paper was to study using this iteration algorithm for the solution of nonlinear Volterra integral equations. It was investigated that the sequences obtained from this iteration algorithm converged to the solution of nonlinear Volterra integral equations. Moreover, data dependence was obtained for nonlinear Volterra integral equations. An example was given that confirmed the applicability of the newly proven theorems. © 2024 the Author(s), licensee AIMS Press.

Volume

9

Issue

7

URI

https://www.scopus.com/record/display.uri?eid=2-s2.0-85194225489&origin=SingleRecordEmailAlert&dgcid=raven_sc_affil_en_us_email&txGid=919467ec76113d61d4496e3212f226d8
https://www.aimspress.com/data/article/preview/pdf/6655b36bba35de1590be3fe7.pdf
https://hdl.handle.net/20.500.12440/6263

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