Durban University of Technology’s (DUT’s) Dr Mathew O. Aibinu was recently awarded the Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) Postdoctoral Fellowship by the National Department of Science and Innovation (DSI) in partnership with the National Research Foundation (NRF).
At the DSI-NRF CoE-MaSS event held recently, Dr Aibinu was recognised for the significance of his research on some of his earlier work done on the Delay Differential Equations (DDEs). One of the hosts congratulated Dr Aibinu saying the CoE-MaSS Postdoctoral Fellowship is very competitive and that it is an amazing and worthy dividend for his hard work. Furthermore, the host recommended that Dr Aibinu’s mathematics skill be used more effectively to support DUT students who may be struggling with understanding concepts. He will co-supervise with the hosts on selected problems that will involve an engineering or computer science application to train the postgraduate students.
Speaking about this achievement, Dr Aibinu expressed his gratitude to the CoE-MaSS for the award and said that it is a motivation for more commitment to excellence.
“I am fascinated with solving optimisation problems by using the fixed-point theory. I also thank my hosts and in particular, DUT’s Deputy Vice-Chancellor: Research, Innovation and Engagement, Professor Sibusiso Moyo for introducing me to some of the applied problems involving Differential Equations and Delay Differential Equations and Symmetry methods as they can be applied to solving Differential Equations. I look forward to working and supporting some of the DUT students who would be interested in applying mathematics to real world problems as part of the Institute for Systems Science and the CoE-MASS postdoctoral fellowship,” said Dr Aibinu.
He relayed that his quest of solving real life problems by using fixed point theory as a mathematical tool started when he joined DUT as a postdoctoral fellow in November, 2019, after completing his PhD in mathematics at the University of KwaZulu-Natal (UKZN).
Furthermore, Dr Aibinu explained that real-life problems can occur in the business, health, built engineering and natural sciences areas, to mention a few.
“Tackling problems that arise in these areas can involve solving optimisation problems with the intention of minimising costs in industrial processes or maximising efficiencies in other systems under observation. It is precisely, for this reason that developing reliable and tested mathematical methods remains a priority focus area that can contribute to build capacity, especially in relation to industry applications and business processes. Using suitable mathematical methods could help to predict, plan and avert some technical difficulties that one encounters when working in this area and helps to reduce waste in certain industrial and business processes,” said Dr Aibinu.
He said many problems which arise from modelling of real-life problems are governed by differential and integral equations. He named heat, wave and Schrödinger equations as typical examples where such evolution equations occur.
Dr Aibinu is interested in the construction of solutions of nonlinear differential and integral equations by reducing them to a problem of finding a fixed point for an operator defined on a subset of a space of such functions. His research addresses the problem of the existence of fixed points of certain operators, by presenting various iteration schemes, which were shown to converge to a fixed point of the given operator.
“Several events in nature are not instantaneous in their occurrences and can therefore be modelled by Delay Differential Equations (DDEs). For instance, modelling of the spread of infectious diseases, population dynamics or electrodynamics problems are guided by DDEs. Finding the conditions for certain DDEs has been demonstrated by several authors in the literature,” said Dr Aibinu.
Pictured: Dr Mathew O. Aibinu