Workshop facilitator

Sandile Motsa
Prof Sandile Motsa
(University of Eswatini)
Title: On the use of LLMs for scientific code generation

Abstract: The workshop will explore the use of large-language model (LLM) tools for developing scripts based on the application of well-defined prompts on the block hybrid method for solving initial-value problems.
Bio: Prof Motsa is currently serving as the Dean of the Faculty of Science and Engineering at the University of Eswatini. He holds Honorary Professorships at the UKZN and Wits University and is a Professor Extraordinaire at UNISA. He is a distinguished Applied Mathematician and a founding member of the Kingdom of Eswatini Academy of Science (KEAS). He specializes in the development of numerical methods for solving mathematical models in Science and Engineering. With over 200 publications and more than 5900 citations, Prof Motsa is an influential researcher and serves on the editorial boards of prestigious journals. He has contributed significantly to the Southern Africa Mathematical Sciences Association (SAMSA) as Vice President and President. He has supervised numerous Postdocs, Doctoral and Master’s students. He is passionate about integrating AI and technology into education and research, regularly sharing his insights through his column "AI Corner" in the Eswatini Observer.

Plenary speakers

Inger Fabris-Rotelli
Prof Inger Fabris-Rotelli
(University of Pretoria)
Title: Spatial Linear Networks in Applications

Abstract: This talk will cover the use of linear networks in Spatial Statistics. A variety of methods will be discussed involving analysis in a linear network space. Applications in informal roads, criminology and disease mapping will be presented.

Bio: Prof Inger Fabris-Rotelli is currently an associate professor in the Department of Statistics, University of Pretoria. She has been at the Department of Statistics since 2004. She holds a PhD Mathematical Sciences, obtained in 2013, an MSc Applied Mathematics, a double BSc (Hons) in Mathematical Statistics and Applied Mathematics and a BSc Applied Mathematics. She has supervised 68 honours, 26 Masters and 7 PhD students to completion, and is currently supervising 10 honours, 6 Masters and 7 doctoral students, and has a particular passion for postgraduate supervision. She has published 33 peer-reviewed journal articles, 26 peer-reviewed conference proceedings papers and 1 book chapter.

She was on the executive of the South African Statistical Association (SASA) from 2012 – 2018, and from 2019-2024 sat as a director on the ICCSSA (Institute of Certificated and Chartered Statisticians in South Africa) board. She is the immediate past-president of SASA and CEO of ICCSSA. She is also a member of ISI and IMS internationally, and the Golden Key Society, SASA, SAMS, GISSA, SAMSA, GASA and RLadies Johannesburg co-chair locally. She is a SACNASP council member elected 2021 – 2025 as well as a SACNASP registered scientist. Her research interests are in spatial statistics and GIS, as well as remote sensing and general image processing, including spatial epidemiology and criminology.

Ashleigh Jane Hutchinson
Dr Ashleigh Hutchinson
(University of Manchester)
Title: Going with the flow: Integrating lab experiments into mathematical modelling

Abstract: It is often thought that mathematical models, where equations are derived using fundamental physical laws, lead to accurate representations of reality. After all, if we base our equations on well-established principles such as the conservation of mass, momentum, and energy, and we find solutions to these equations which are exact or numerical with an acceptably small margin of error, what could possibly go wrong? In this talk, we will examine several mathematical models that describe the behaviour of slow-moving viscous fluids in confined geometries. I will then reveal what happens when these models are tested against laboratory experiments. As we compare theory to experiment, we will discover that even when our models are built on solid physical foundations, they can neglect crucial factors that significantly impact real-world behaviour. As a result, even a small set of laboratory experiments can play a crucial role in understanding why mathematical models may fail to represent reality. I will show how experiments and theory can be used in tandem, where lab experiments can assist in identifying missing physical mechanisms, narrowing our focus, and ultimately resulting in mathematical models that are a better representation of reality.

Bio: Dr Ashleigh Jane Hutchinson is a Lecturer in Applied Mathematics at the University of Manchester, UK. In 2016 she earned her PhD from the University of the Witwatersrand, Johannesburg, South Africa. In 2021, she was awarded a prestigious Newton International Fellowship, allowing her to conduct research at Cambridge University, UK. Her research is primarily focused on fluid mechanics, particularly problems involving low-Reynolds number flows and non-Newtonian fluids, which have a variety of applications in both nature and industry. Dr Hutchinson’s approach to solving complex problems is multidisciplinary, combining theoretical modelling, laboratory experiments and numerical simulations. In addition to fluid dynamics, she has a keen interest in other areas of applied mathematics, including population dynamics, energy conservation, and mining.

Abdul Kara
Prof Abdul Kara
(University of the Witwatersrand)
Title: Symmetries & Conservation Laws of differential equations - alternate approaches and extensions

Abstract: The relationship between symmetries and conservation laws has been a subject of interest during the 1800s and culminated in Noether's Theorem of 1918 for variational DEs. In this presentation, we discuss this relationship with alternate approaches, e.g., 'partial Lagrangians' and Noether type operators. We also consider the extension of this relationship to DEs with 'small parameters via approximate symmetries', discrete equations and fractional DEs.

Bio: Abdul H Kara completed all his studies at Wits University and in all, but one year, has been at Wits from Junior Lecturer through to Professor; the one year being served as a school teacher. His PhD thesis involved a range of topics around the Symmetries of Differential Equations, Euler-Lagrange equations and their relationship with Conservation Laws. Abdul has published with collaborators from China, the US, Russia, Pakistan and with his students from SA and abroad. He continues to apply his work in mathematical physics, engineering and relativity and extend his ideas to Discrete Equations and Fractional Differential Equations.

Nordstrom Nordstrom
Prof Jan Nordstrom
(Linköping and UJ)
Title: Linear and Nonlinear Boundary Conditions: What's the difference?

Abstract: We present a straightforward energy stable weak implementation procedure of open boundary conditions for initial boundary value problems. The new boundary procedure generalize the well-known characteristic boundary procedure for linear problems to the nonlinear setting. We discuss the differences and exemplify with boundary conditions for the shallow water equations, the Euler and Navier-Stokes equations and equations for multi-phase flows.

Bio: Jan Nordström is Professor Emeritus in Computational Mathematics at the Department of Mathematics, Linköping University, Sweden, a Distinguished Visiting Professor at the Department of Mathematics and Applied Mathematics, University of Johannesburg, South Africa and an Honorary Professor in Computational Mathematics at University of Cape Town, South Africa. He is also a member of the Academy of Science of South Africa. His main interest is in Initial Boundary Value Problems (IBVPs), and in particular the fundamental effect of boundary and interface conditions on well-posedness and stability. He stresses the necessity to understand the IBVP during the development of numerical approximations.