Seminars

Bio-Sketch: Dr Andrea Thomann has a permanent position at Inria (National Institute for Research in Digital Science and Technology hosted by the Université de Strasbourg, France. She earned her PhD at the University of Insubria in Como (Italy), where she worked on numerical schemes for Euler equations in the low Mach regime. Her research is dedicated to the development of a numerical scheme for multi-scale fluid dynamics that is valid for all Mach number regimes. One challenge is deriving a numerical scheme that mimics the transition between compressible and incompressible regimes as the Mach number goes to zero and preserves further structures of the underlying model. Over the years, she has developed implicit-explicit (IMEX) Runge-Kutta methods based on a Suliciu relaxation model and MOOD technique. She has also contributed significantly to the development of well-balanced schemes for hyperbolic equations and hyperbolic thermodynamically compatible numerical schemes. She is the 2026 Richard-von-Mises Award winner of GAMM (International Association of Applied Mathematics and Mechanics).

Abstract: Multi-scale problems are omnipresent in environmental and industrial processes, posing a challenge to classical numerical solvers given that the propagation speeds of information span several orders of magnitude. In hyperbolic systems, the absolute fastest wave speed remains finite,
but in classical, explicitly integrated numerical schemes, it determines the time step that ensures stability. This means in particular that it may lead to vanishing time increments in the presence of fast processes caused for instance by high pressure or strong magnetic fields. Furthermore, it is known that upwind schemes introduce spurious numerical diffusion into the approximate solution, a problem that can only be partially mitigated by mesh refinement. Therefore, a common approach, which will be also applied here, is to use implicit or semi-implicit time integrators, combined with a suitable
approximation of spatial derivatives in the implicitly treated systems. This allows scale-independent artificial dissipation and stability to be obtained under large time steps. As the evolution of the modeled variables is described by a nonlinear flux function, treating it fully or partially implicitly involves solving nonlinear systems. Depending on the problem, these systems can be large, coupled and ill-posed, for which solvers such as the Newton method may converge very slowly or not at all. To avoid nonlinear implicit systems, we apply a subtle linearization while keeping the systems compatible with crucial properties such as asymptotic limits, conservation of mass, momentum and energy, and necessary vector-calculus identities. In this talk, the construction of such numerical schemes in the finite volume framework will be illustrated at the example of a model of continuum mechanics. 

Keywords: Hyperbolic systems of balance laws, multiscale, finite volume schemes, implicit-explicit schemes, structure preserving. 

Target Audience: Researchers, undergraduates, and graduate students in numerical analysis and applied mathematics.

Bio-Sketch: Patrick Farrell is a Professor in the numerical analysis group at the University of Oxford, and (for 2025-2026) the Donatio Universitatis Carolinae Chair in the faculty of mathematics and physics at Charles University in Prague. His research interests are in the numerical solution of partial differential equations arising in physics and chemistry. He is also employed as a specialist consultant at the UK Atomic Energy Authority. He obtained his bachelor’s degree in mathematics from the University of Galway, and his doctorate from Imperial College London in 2010. His doctoral thesis won the Roger Owen prize from the UK Association for Computational Mechanics and the Janet Watson prize from Imperial. He has been awarded an EPSRC Early Career Research Fellowship (2013-2018), the 2015 Wilkinson Prize for Numerical Software, second place in the 2015 Leslie Fox Prize in Numerical Analysis, the 2020 Charles Broyden Prize in optimisation, a 2021 Whitehead Prize from the London Mathematical Society, and the 2025 SIAM Germund Dahlquist Prize. In 2026 he was elected a Fellow of the Society for Industrial and Applied Mathematics. He gave an invited section lecture at the International Congress of Mathematicians in 2026.

Abstract: Initial-value problems for ordinary and partial differential equations often possess conservation laws (e.g. for energy) and dissipation inequalities (e.g. for entropy). Standard discretisation methods, such as many Runge-Kutta and multistep schemes, usually do not preserve these structural properties. In this talk, we present a general strategy for simultaneously enforcing multiple conservation laws and dissipation inequalities in the numerical solution of initial-value problems. The key idea is to systematically modify a starting discretisation so that the continuous arguments establishing conservation and dissipation carry over to the discrete level. Each conservation law or dissipation inequality is represented by an associated test function; we introduce auxiliary variables for the projections of these test functions onto a discrete test set, and modify the equation to use these new variables. We demonstrate this strategy by applying it to Hamiltonian ordinary and partial differential equations, geometric flows, the incompressible and compressible Navier-Stokes equations, and a viscoelastic model. In each case, the strategy yields discretisations with new and useful properties. In several cases, preserving conservation and/or dissipation laws appears to offer considerable qualitative advantages over preserving other structures, such as symplecticity.

Keywords: Conservation laws, Dissipation, Hamiltonian, Navier-Stokes, Geometric flows,  Symplecticity.

Target Audience: Researchers, undergraduates, and graduate students in numerical analysis and applied mathematics.

“Integrating Numerical Analysis and Machine Learning for Predictive Modelling of Complex Engineering Systems”

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Samuel O. Essang, Ph.D. 

Department of Physical Science, Landmark University, Nigeria. 

Abstract: Complex engineering systems often require repeated high-cost simulations before reliable decisions can be made. This seminar examines how numerical analysis can be integrated with machine learning to improve predictive accuracy and reduce computational effort. Using recent studies on high-temperature heat pipes, expansive-soil road widening, and offshore wind-turbine monopile foundations, the discussion compares finite-element analysis, computational fluid dynamics, coupled hydro-mechanical modelling, artificial neural networks, and random forests. Particular attention is given to model formulation, data generation, validation, error assessment, and the conversion of numerical outputs into efficient surrogate models. The seminar also considers the limitations of data-driven prediction, including dependence on training data, extrapolation risk, and physical inconsistency. The central argument is that hybrid numerical and machine-learning frameworks are most useful when mathematical structure, physical laws, and empirical validation are retained. These methods can support safer infrastructure, efficient energy systems, and sustainable engineering decisions.  

Keywords: Numerical analysis; Machine learning; Finite-element analysis; Predictive modelling; Sustainable engineering; SDG 3; SDG 7     

Bio-Sketch: Samuel O. Essang is a Mathematics Lecturer in the Mathematics Programme, Department of Physical Science, Landmark University, Omu Aran, Nigeria. His research interests lie in convex optimization, mathematical modelling, data science, and machine learning. His scholarly work applies mathematical and computational methods to optimization algorithms, neural networks, artificial intelligence, predictive modelling, and interdisciplinary scientific problems. His current interests include integrating numerical analysis and machine learning to improve simulation, prediction, and decision support in engineering, energy, and health-related systems. 

“Advanced Exponential and Multirate Integrators for Multiple Time Scale Problems”

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Vu Thai Luan, Ph.D. 

Department of Mathematics & Statistics, Texas Tech University, USA. 

Abstract: Many science and engineering problems involve multiple physical processes, with complex interactions that result in dynamics spanning a wide range of time scales.  This presents significant challenges for real-time simulation of these multiphysics problems. A prominent example is the existence of vastly differing time scales in atmospheric phenomena, ranging from a relatively slow advection to very fast gravity waves, which poses significant difficulties for real-time simulation of weather and long-term climate predictions. Developing fast and accurate time integration methods is thus crucial for a wide range of applications that rely on simulations of complex multiphysics systems. In this talk, we will present our recent advancements in constructing, analyzing, and implementing new exponential and multirate time integration methods. These methods enhance both accuracy and efficiency in computational simulations of large-scale, multiple time scale problems. We will also showcase their performance through numerical experiments across various applications, including visual computing, numerical weather prediction, and computational biology.  

Keywords: Exponential RK methods; Multirate time integration; Stiff order conditions; Multiple Time Scale.    

Bio-Sketch: Dr. Luan is an Associate Professor in the Department of Mathematics & Statistics at Texas Tech. He received his Ph.D. in Applied Mathematics from the University of Innsbruck in 2014. Prior to joining Texas Tech, he held faculty positions at Mississippi State University and visiting appointments at University of California, Merced and Southern Methodist University. His research lies in numerical analysis and scientific computing, with a focus on the development of high-order time integration methods for stiff and highly oscillatory systems such as exponential integrators, multirate methods, and two-derivative schemes, with applications in numerical weather prediction, visual computing, and computational biology. He has been the principal investigator of several grant awards by NSF. He serves as an Associate Editor for Advances in Applied Mathematics and Mechanics and has actively contributed to the organization of scientific conferences/workshops and summer schools. 

“Runge-Kutta Discontinuous Galerkin Methods Beyond the Method of Lines”

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Yulong Xing, Ph.D. 

The Ohio State University, Columbus, Ohio, USA. 

Abstract: In the common practice of the method-of-lines (MOL) approach for discretizing a time-dependent partial differential equation (PDE), one first applies spatial discretization to convert the PDE into an ordinary differential equation system. Subsequently, a time integrator is used to discretize the time variable. When a multi-stage Runge-Kutta (RK) method is used for time integration, by default, the same spatial operator is used at all RK stages. However, recent studies on perturbed RK methods indicate that not all RK stages are born equal – breaking the MOL structure and applying rough approximations at specific RK stages may not affect the overall accuracy of the numerical scheme. In this talk, we present two of our recent explorations on blending rough stage operators in RK discontinuous Galerkin (DG) methods for solving hyperbolic conservation laws. In our first work, we mix the DG operator with the local derivative operator, yielding an RKDG method featuring compact stencils and simple boundary treatment. In our second work, we mix the DG operators with polynomials of degrees k and k-1, and the resulting method may allow larger time step sizes and fewer floating-point operations per time step.  

Keywords: Runge--Kutta method, hyperbolic conservation laws, discontinuous Galerkin method, Fourier-type analysis.    

Bio-Sketch: Dr. Yulong Xing is a professor in the Department of Mathematics at the Ohio State University. He received his bachelor degree from University of Science and Technology of China in 2002, and Ph.D. in Mathematics from Brown University in 2006 under the supervision of Prof. Chi-Wang Shu. Prior to joining OSU, he worked as a Postdoctoral Researcher at Courant Institute, New York University, a staff scientist at Oak Ridge National Laboratory, a joint assistant professor at University of Tennessee Knoxville, and an assistant professor at University of California Riverside. He works in the area of numerical analysis and scientific computing, wave propagation, computational fluid dynamics. His research focuses on the design, analysis and applications of accurate and efficient numerical methods for partial differential equations. He has received a CAREER Award from the National Science Foundation. 

“Hybrid methods for elliptic PDEs: Enriching continuous Lagrange finite element approximation spaces”

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Victor Michel-Dansac, PhD. 

Institut de Recherche Mathématique Avancée, Strasbourg, France. 

Abstract: To goal of this talk is to introduce a study combining two approaches in the context of solving PDEs: the continuous finite element method (FEM) and more recent techniques based on neural networks. In recent years, physics-informed neural networks (PINNs) have become particularly interesting for rapidly solving PDEs, especially in high dimensions. However, their lack of accuracy can be a significant drawback, hence the interest in combining them with FEM, for which error estimates are already known. In the first part of the talk, we introduce a general framework to unify neural methods (PINNs, etc) and classical ones (FEM, etc) under the same formalism. Namely, we define both neural and classical methods as (Petrov-)Galerkin projections on suitable function spaces. The goal is to gently introduce the audience to neural methods, and to highlight the differences and similarities with classical ones. In the second part of the talk, consisting in original work, we modify the classical FEM approximation spaces by taking information from a prior, chosen as the prediction of a neural network. On the one hand, this combination improves and certifies the prediction of neural networks, to obtain a fast and accurate solution. On the other hand, error estimates are proven, showing that such strategies outperform classical ones by a factor that depends only on the quality of the prior. We validate our approach with numerical results performed on parametric problems with 1D, 2D and 3D geometries. These experiments demonstrate that to achieve a given accuracy, a coarser mesh can be used with our enriched FEM compared to the standard FEM, leading to reduced computational time, particularly for parametric problems. 

Keywords: Petrov-Galerkin, PINNs, FEM, Scientific machine learning, Neural networks.   

Bio-Sketch: Dr. Victor Michel-Dansac works as a permanent researcher (ISFP, INRIA Starting Faculty Position) in the project-team MACARON of the Inria Strasbourg research center, located at IRMA (Institut de Recherche Mathématique Avancée), in Strasbourg, France, since 2020. He earned his PhD from LMJL, Nantes, in September 2016. Following his Ph.D., he embarked on a postdoctoral journey, first at IMT, Toulouse, from October 2016 to August 2017, and then at IMT (INSA), Toulouse, from September 2017 to August 2020. Dr. Michel-Dansac's contributions to the field have been recognized through grants such as the ANR JCJC project called SMEAGOL. His research areas encompass several topics, including scientific computing and the development of numerical schemes. Since he arrived in Strasbourg, he has started to work in the area of Scientific Machine Learning, enhancing numerical schemes with techniques from machine learning. 

“Discrete-time optimal control of species augmentation for predator–prey model”

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Dasumani Munkaila, PhD. 

Pan African University Institute for Basic Sciences, Technology and Innovation (PAUSTI) 

Abstract: This talk presents a discrete-time optimal control theory applied to two models of species augmentation for predator–prey relationships. In discrete time models, the order in which events occur can give different qualitative results. Two models representing different orders of events of optimal augmentation timing are considered. In one model, the population grows and predator–prey action occurs before the translocation of reserve species for augmentation. In the second model, the augmentation happens first and is followed by growth and then predator–prey action. The reserve and target populations are subjected to strong Allee effects. Optimizations in the two models are solved numerically using the discrete version of the forward–backward sweep method and the sequential quadratic programming iterative method, respectively. This work represents the first optimal augmentation results for models incorporating the predator–prey relationship with discrete events.   

Keywords: Discrete-time models; Forward-backward sweep method; Order of events; Predator-prey interaction; Sequential quadratic programming; Species augmentation.   

Bio-Sketch: Dr. Dasumani Munkaila is a Ghanaian mathematician who earned his Master’s degree in Applied Mathematics from Kwame Nkrumah University of Science and Technology (KNUST) and holds a Bachelor’s degree from the University of Cape Coast (UCC). He recently completed his PhD in Applied Mathematics at the Pan-African University Institute for Basic Sciences, Technology and Innovation (PAUSTI), hosted at Jomo Kenyatta University of Agriculture and Technology in Nairobi, Kenya. Having successfully fulfilled his doctoral requirements and received his official PhD award letter, he is currently awaiting graduation. Munkaila’s research expertise lies at the intersection of Mathematical Biology, Ecology, and Optimal Control Theory. His work utilizes numerical modeling techniques, including Ordinary Differential Equations (ODEs), Discrete Difference Equations, and Fractional Calculus, to address complex biological challenges. 

“Fluid Instabilities in Stratified Systems: The Role of Chemistry and Diffusion ”

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Johnson Olubori Oyero, PhD. 

Université Libre de Bruxelles, Belgium 

Abstract: Mixing between density-stratified fluids in a gravitational field is often driven by buoyancy-induced hydrodynamic instabilities. This talk examines how chemical reactions and differential diffusion influence such instabilities in miscible fluid systems. Using numerical simulations of the Navier–Stokes equations coupled with reaction–diffusion equations, we show how these processes modify density profiles and can trigger or intensify convection. The results illustrate how chemical composition and transport properties control the onset and dynamics of buoyancy-driven mixing.   

Keywords: Stratified flows; buoyancy-driven instabilities; reacting flows; double-diffusive instability; Navier–Stokes equations; spectral element method; direct numerical simulation.  

Bio-Sketch: Dr. Johnson Olubori Oyero received his Ph.D. from the Université Libre de Bruxelles (Belgium) in December 2025. His research lies at the interface of computational fluid dynamics, nonlinear dynamics, and physical chemistry, with a focus on modeling heat and mass transfer in multiphase and reactive fluid systems. His work investigates how chemical reactions, diffusion, and buoyancy interact to generate and control hydrodynamic instabilities and pattern formation in stratified fluids. Through mathematical modeling and high-resolution numerical simulations, his research aims to improve the prediction and control of mixing processes in environmental, industrial, and geophysical flows. He has presented his work at several international conferences and seminars. 

“Numerical solution of an associated Fokker-Planck equation for uncertainty quantification in rainfall-runoff systems ”

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Ezéckiel Houénafa Sianou, PhD. 

Pan-African University, Nairobi, Kenya

Abstract:  This talk uses a stochastic differential equation (SDE) framework to investigate aleatoric uncertainty in rainfall–runoff systems. The associated Fokker–Planck equation is solved numerically with an adaptive finite difference method to characterize the temporal evolution of discharge probability densities. Uncertainty is quantified from these densities using Quantile Intervals and a High-Probability Region method based on Simpson’s 1/3 rule.  

Keywords: SDE, Fokker-Planck equation, uncertainty, adaptive finite difference, Simpson’s 1/3 rule 

MSC Classification: Primary 81S25; Secondary 60H10, 60H20, 65U05.

Bio-Sketch: The speaker received his Ph.D. from the Pan-African University in December 2025, with expertise in computational mathematics, hydrological modeling, stochastic modeling, and hybrid Physics-AI methods. His research focuses on advancing hydrological modeling through stochastic dynamics and hybrid approaches integrating machine learning. His work has led to methodological developments that support the anticipation of floods and droughts and the planning of water resources. He has presented his research at international seminars and shared his findings with the Africlimate AI community. 

“Numerics for Quantum Stochastic Differential Equations and Inclusions”

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Dauda Alani Dikko, Ph.D.

University of Ibadan, Nigeria

Abstract:  In this talk, we introduce the theoretical framework of the Hudson-Parthasarathy Quantum Stochastic calculus by Hudson and Parthasarathy (1984) as extended by Ekhaguere (1992). We shall then present a rigorous review of some of the existing results by Ayoola (2002) and J.O. Adeyeye (2007), where some of the numerical schemes of quantum stochastic differential equation (QSDE) within this framework are discussed.  

Keywords: Quantum stochastic Processes, Numerical QSDE’s.

MSC Classification: Primary 81S25; Secondary 60H10, 60H20, 65U05.

Bio-Sketch: The speaker had his Ph.D. from the University of Ibadan, with core expertise in Stochastic analysis and its applications. Quantum Probability, Quantum information and communication processes, Quantum computing, Finance and Computational Mathematics. His doctoral research was a study on establishing existence results for a class of Quantum Stochastic Differential inclusions(QSDI) which employ the strong operator topology generated by the strong family of semi norm to investigate existence and convexified problem of a class of QSDI in a locally convex space of operator observables whose topology is generated by a strong family of semi norm defined via the norm of the Fock space. He has presented his research at both local and international conferences. He was awarded an African hero and an outstanding lecturer of the year in 2023 by the Global Skills Hub, United kingdom. 

“PDEs on Curved and Non-Smooth Surfaces: A New Framework and its Numerical Analysis”

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Marcial Nguemfouo, PhD

University of Yaounde, Cameroon

Abstract:  Partial Differential Equations on surfaces are crucial for modeling phenomena in fluid dynamics, biology, and materials science. However, standard numerical theories often fail for non-smooth geometries like polyhedra. In this talk, we introduce a new theoretical framework based on Lipschitz manifolds to bridge this gap. The core of our approach is the development of a full calculus—including Stokes' and Green's theorems—on these non-smooth surfaces, establishing the well-posedness of the Poisson problem. We will then present a rigorous analysis of the Finite Element Method on closed surfaces, deriving a new upper bound for the condition number of the resulting linear system. Our numerical results demonstrate optimal convergence rates not only on smooth surfaces like the sphere but also on non-smooth Lipschitz manifolds like the surface of a cube. 

Keywords: Laplace-Beltrami Operator, Lipschitz Manifolds, Surface FEM, Numerical PDEs.

MSC Classification: Primary 65N30; Secondary 58J05, 65N22

Bio-Sketch: A highly accomplished PhD Mathematician with a core expertise in the analysis and numerical simulation of Partial Differential Equations (PDEs) on surfaces and manifolds. My doctoral and post-doctoral research established a rigorous foundation in the finite element method for geometric operators, with a specific focus on the well-posedness and numerical conditioning of the Laplace-Beltrami operator on complex geometries. This strong theoretical base is complemented by a proven ability to apply advanced mathematical techniques to solve complex, real-world problems across diverse fields. My interdisciplinary research portfolio includes developing epidemiological models for public health (COVID-19, under-5 mortality), collaborating with leading oncology institutes on mathematical models of cancer, designing neural networks for financial strategy optimization, and applying network science to social and agricultural systems. He is proficient in Python, R, MATLAB, and scientific software like SALOME and ParaView. He has presented his research both local and international conference.

“Some Real-World Applications of Numerical Optimization”

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Prof. Abubakar Sani Halilu

Sule Lamido University, Nigeria

Abstract:  In recent years, iterative methods have found extensive application in numerical optimization, particularly for restoring disturbed signals and images in compressive sensing. To enhance restoration quality, this research proposes a conjugate gradient projection algorithm for solving constrained monotone nonlinear equations. The key idea of the proposed algorithm is to approximate the Jacobian matrix using an acceleration parameter, thereby enabling the formulation of an effective conjugate gradient parameter. The method is applied to the ℓ₁-norm regularization problem in signal recovery and image restoration, demonstrating improved performance over existing methods as reported in the literature.

Keywords: Acceleration parameter, Conjugate gradient method, Signal recovery, Image restoration, Jacobian matrix, Nonlinear monotone equations.

MSC Classification: Primary 65K05; Secondary 90C30, 90C53

Bio-Sketch: Dr. Abubakar Sani Halilu obtained his Ph.D in Mathematics from Lovely Professional University, India, and holds both B.Sc. and M.Sc. degrees in Mathematics from Bayero University, Kano, Nigeria. He is currently a Lecturer in the Department of Mathematics at Sule Lamido University, Kafin Hausa, Nigeria, and a member of the Numerical Optimisation Research Group at Bayero University, Kano. Dr. Halilu is also serving as a Postdoctoral Researcher at Universiti Sultan Zainal Abidin, Malaysia. He has published numerous articles in reputable journals indexed in the Web of Science and Scopus, with over 650 citations on Google Scholar. 

“Neural ODEs for parameter estimation and simulation of some selected prevalent diseases models in Africa”

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Festa Ndubuogaranya

University of Lagos, Nigeria

Abstract: This study explores the application of Neural Ordinary Differential Equations (Neural ODEs) in simulating and estimating parameters for the spread of some selected prevailing diseases in Africa, focusing on COVID-19, malaria, tuberculosis, and HIV/AIDs. The main objective of this study was to forecast the future disease spread, which was achieved by employing the trained neural ODEs model. The model applies a data driven and numerically informed approach to predict the behaviour of the disease transmission through the combination of epidemiological data and disease informed neural network. The predictions for COVID-19 and malaria are based on real life data, while transmission dynamics of HIV/AIDs and tuberculosis are generated using the 4th order Runge-Kutta methods to simulate the behaviour of these diseases. Results show that the neural networks are capable of learning the spread of the diseases, accurately captures the disease spread and progression patterns of each diseases' compartment,  estimates their unique parameters, and forecasting the future trends of this diseases from observed real life data and numerically generated data. It is observed that the higher the number of epoch, the better the predictions of the spread of each diseases. Higher epoch allows the model to capture the complex progressions and fluctuations of the compartments of each diseases which aligns well with the original epidemiological data. One limitation observed is that increasing the number of epochs, while beneficial for model accuracy, significantly extends the training duration, sometimes into several hours.

Keywords: Neural ODEs, Neural Network, Epidemiology, Compartmental Model, Runge Kutta Method.

Biosketch: Festa Ndubuogaranya is a research assistant and a Ph.D. student in Computational and Applied Mathematics. Her research interest lies in computational mathematics, scientific computing, and machine learning, with a particular focus on the development of high-order numerical algorithms and deep learning techniques for the modeling of complex dynamical systems. Her research interest also extends to the numerical simulation of differential equations arising from air-pollution modelling, epidemiology, fluid-structure interactions, and wave propagation. She has participated in international conferences and workshops across mathematics and diverse scientific fields, where she has presented her research work and engaged with scholars working on interdisciplinary challenges. 

“Recent advances in the numerical solution of fractional differential equations”

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Prof. Luigi Brugnano

University of Florence, Italy

Abstract: The numerical solution of fractional differential equations has gained more and more attention in the last years, due to their increasing use in applications. Numerical software, aimed at solving such equations, has to cope with a number of intrinsic difficulties stemming from the possible non-smoothness of the solution, and/or the vector field, at the initial point. Moreover, the non-locality of the operator poses additional challenges due to the fact, at any point, the solution depends on all its past values and, consequently, the computational cost increases. Recently, a class of methods, name Fractional HBVMs (FHBVMs) has been derived for the efficient numerical solution of fractional differential equations of Caputo type. In case of an integer derivative, such methods reduce to HBVMs, a class of Runge-Kutta methods formerly devised for the efficient numerical solution of Hamiltonian problem. The basic idea, on which these latter methods rely on, is the local expansion of the vector field along the Legendre orthonormal polynomial basis which, in the case of a fractional derivative, becomes a suitable orthonormal Jacobi polynomial one, from which FHBVMs are derived. In this talk, we shall recall the main facts about FHBVMs, which have been implemented in two MATLAB codes, also showing their effectiveness through comparisons with existing MATLAB solvers.

Keywords: fractional differential equations, FDEs, Caputo derivative, Fractional HBVMs, FHVBMs, MATLAB software.

MSC Classification: 34A08, 65R20,65-04. 

Biosketch: Luigi Brugnano started his career at the University of Bari, Italy, in 1990. In 1992 he moved, as an associate professor, at the University of Florence, Italy, where, in 2001 he became full professor of Numerical Analysis. Since 1996, he is based at the Mathematics and Informatics Department of that University. He is author of two research monographs and over 160 scientific publications. His main contributions concern Numerical Linear Algebra and the Numerical Solution of Differential Equations.

“Block methods for solving initial and boundary value differential problems”

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Dr. Mufutau Ajani Rufai

Free University of Bozen-Bolzano, Italy

Abstract: In this talk, I will present block methods for solving initial and boundary value differential problems. I will use a suitable polynomial to approximate the theoretical solution of the problems under consideration. I will also present the theoretical analysis of the basic characteristics of the proposed methods. Several real-life first-order, second-order, and third-order singular and non-singular IVPs and BVPs model differential problems in applied sciences and engineering, including stiff and Lane-Emden-Fowler type equations, will be integrated numerically to determine the efficiency of the proposed methods.

Keywords:  Block Methods; Ordinary and Time-Dependent Partial Differential Equations; Initial and Boundary Value Problems; Lane-Emden Type Equations; Stability and Convergence Analysis.

MSC Classification: 65L05, 65L20; 65L80

Biosketch: Dr. Mufutau Ajani Rufai obtained his Ph.D. from the University of Bari, Aldo Moro, Italy, in 2022. The award of the Ph.D. was strongly supported by the two external examiners, who each assessed the Thesis as excellent from all points of view. The award of the Doctorate in Computer Science and Mathematics with Cum Laude qualification was the unanimous recommendation of the examiners. Currently, he holds a postdoctoral researcher position at the Free University of Bozen-Bolzano in Italy. He has actively participated in international conferences and workshops and authored many scientific research papers on numerical solutions for differential problems. His research interest lies in Applied Mathematics and focuses on Numerical Analysis, Differential Equations and Applications, Computational Mathematics, and Optimization.

“A space–time continuous and coercive formulation for the wave equation”

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Dr. Andrea Moiola

Department of Mathematics, University of Pavia, Italy

Abstract: We propose a new space-time variational formulation for wave equation initial-boundary value problems. The key property is that the formulation is coercive (sign-definite) and continuous in a norm stronger than H^1(Q), Q being the space-time cylinder. Coercivity holds for constant-coefficient impedance cavity problems posed in star-shaped domains, and for a class of impedance–Dirichlet problems. The formulation is defined using simple Morawetz multipliers and its coercivity is proved with elementary analytical tools, following earlier work on the Helmholtz equation. The formulation can be stably discretised with any H^2(Q)-conforming discrete space, leading to quasi-optimal space-time Galerkin schemes. Several numerical experiments show the excellent properties of the method. This is a joint work with Paolo Bignardi; see arXiv:2312.07268 

Keywords:  Wave equation, Variational formulation, Coercivity, Sign-definiteness, Morawetz multiplier, Morawetz identity, Quasi-optimality, Galerkin method, Finite element method.

MSC Classification: 35L05, 65M60, 65M15

Biosketch: Andrea Moiola received a PhD in Mathematics at the ETH Zurich (Switzerland) in 2011. He was then research fellow at the University of Reading (UK) until 2017, when he moved to the University of Pavia (Italy), where he is currently associate professor. His research focuses on numerical methods for the approximation of wave propagation, in particular on Trefftz-discontinuous Galerkin, boundary element, and space-time methods.

Research Paper: iris.unipv.it/handle/11571/1519237