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A novel iterative scheme for solving delay differential equations and third order boundary value problems via Green's functions

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dc.contributor.authorGodwin Amechi Okeke
dc.contributor.authorAkanimo Victor Udo
dc.contributor.authorAlqahtani, Rubayyi T.
dc.contributor.authorMelike Kaplan
dc.contributor.authorEltayeb Ahmed, W.
dc.date.accessioned2026-01-04T19:55:41Z
dc.date.issued2024-01-01
dc.description.abstract<abstract><p>In this paper, we constructed a novel fixed point iterative scheme called the Modified-JK iterative scheme. This iteration process is a modification of the JK iterative scheme. Our scheme converged weakly to the fixed point of a nonexpansive mapping and strongly to the fixed point of a mapping satisfying condition (E). We provided some examples to show that the new scheme converges faster than some existing iterations. Stability and data dependence results were proved for this iteration process. To substantiate our results, we applied our results to solving delay differential equations. Furthermore, the newly introduced scheme was applied in approximating the solution of a class of third order boundary value problems (BVPs) by embedding Green's functions. Moreover, some numerical examples were presented to support the application of our results to BVPs via Green's function. Our results extended and generalized other existing results in literature.</p></abstract>
dc.description.urihttps://doi.org/10.3934/math.2024315
dc.description.urihttps://doaj.org/article/5a57b02c8f3e4bbc88a4dee8ff0d2f4e
dc.identifier.doi10.3934/math.2024315
dc.identifier.endpage6498
dc.identifier.issn2473-6988
dc.identifier.openairedoi_dedup___::f4a12f513d3a2bf1b684a0886d545b62
dc.identifier.orcid0009-0009-5243-9991
dc.identifier.orcid0000-0001-5700-9127
dc.identifier.scopus2-s2.0-85184167270
dc.identifier.startpage6468
dc.identifier.urihttps://hdl.handle.net/20.500.12597/41462
dc.identifier.volume9
dc.identifier.wos001162931900007
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)
dc.relation.ispartofAIMS Mathematics
dc.rightsOPEN
dc.subject$ \mathcal{j} $-stability
dc.subjectdelay differential equations
dc.subjectfixed point
dc.subjectboundary value problems
dc.subjectmodified-jk iterative scheme
dc.subjectQA1-939
dc.subjectcondition (e)
dc.subjectMathematics
dc.subjectrate of convergence
dc.subjectgarcia-falset mapping
dc.titleA novel iterative scheme for solving delay differential equations and third order boundary value problems via Green's functions
dc.typeArticle
dspace.entity.typePublication
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