A new iteration method for the solution of third-order BVP via Green's function


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AYDIN AKGÜN F. , Rasulov Z.

Demonstratio Mathematica, vol.54, no.1, pp.425-435, 2021 (Journal Indexed in SCI Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1515/dema-2021-0031
  • Journal Name: Demonstratio Mathematica
  • Journal Indexes: Science Citation Index Expanded, Emerging Sources Citation Index, Scopus, Academic Search Premier, Linguistic Bibliography, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.425-435
  • Keywords: boundary value problem, fixed point iteration method, Green's function, integral operator, rate of convergence, MULTIPLE POSITIVE SOLUTIONS, EXISTENCE

Abstract

© 2021 Fatma Aydln Akgun and Zaur Rasulov, published by De Gruyter.In this study, a new iterative method for third-order boundary value problems based on embedding Green's function is introduced. The existence and uniqueness theorems are established, and necessary conditions are derived for convergence. The accuracy, efficiency and applicability of the results are demonstrated by comparing with the exact results and existing methods. The results of this paper extend and generalize the corresponding results in the literature.