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Paper's Title:
D-Iterative Method for Solving a Delay Differential Equation and a Two-Point Second-Order Boundary Value Problems in Banach Spaces
Author(s):
Francis Akutsah1, Akindele Adebayo Mebawondu2, Oluwatosin Babasola3, Paranjothi Pillay4 and Ojen Kumar Narain5
1School
of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: 216040405@stu.ukzn.ac.za,
akutsah@gmail.com
2School
of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS),
Johannesburg,
South Africa.
Mountain Top University,
Prayer City, Ogun State,
Nigeria.
E-mail: dele@aims.ac.za
3Department
of Mathematical Sciences,
University of Bath,
Claverton Down,
Bath, BA2 7AY
UK.
E-mail: ob377@bath.ac.uk
4School
of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: pillaypi@ukzn.ac.za
5School
of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: naraino@ukzn.ac.za
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.
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