D-ITERATIVE METHOD FOR SOLVING A DELAY DIFFERENTIAL EQUATION AND A TWO-POINT SECOND-ORDER BOUNDARY VALUE PROBLEMS IN BANACH SPACES

Francis Akutsah, Akindele Adebayo Mebawondu, Oluwatosin Babasola, Paranjothi Pillay, Ojen Kumar Narain

Research output: Contribution to journalArticlepeer-review

Abstract

The purpose of this paper is to re-establish the convergence, stability and data dependence results established by [2] and [3] by removing the strong assumptions imposed on the sequences which were used to obtain their results. In addition, we introduced a modified approach using the D-iterative method to solve a two-point second-order boundary value problem, and also obtain the solution of a delay differential equations using the obtained results in this paper. The results presented in this paper do not only extend and improve the results obtained in [2, 3], it further extends and improve some existing results in the literature.

Original languageEnglish
Article number6
JournalAustralian Journal of Mathematical Analysis and Applications
Volume19
Issue number2
Publication statusPublished - 23 Sept 2022

Bibliographical note

Funding Information:
The second author acknowledges with thanks the bursary and financial support from Department of Science and Technology and National Research Foundation, Republic of South Africa Centre of Excellence in Mathematical and Statistical Sciences (DST-NRF CoE-MaSS) Postdoctoral Fellowship. The third author also acknowledge the support of the ESPRC Centre for Doctoral Training in Statistical Applied Mathematics at Bath (SAMBa), under the project EP/L015684/1. Opinions stated and conclusions reached are solely those of the author and should not be ascribed to the CoE-MaSS in any way.

Keywords

  • D-iteration
  • Delay differential equations
  • Fixed point
  • Iterative scheme

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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