Irish Mathematical Society

ICEDIM Seminars

Date: Wednesday, 20 November 2024 at 2pm (UTC+00:00)

Speaker: Natalia Kopteva (Limerick)

Title: Time-fractional subdiffusion equations: gentle introduction, regularity, maximum principles, and numerical analysis

Location: Online via Zoom [ Meeting ID: 934 8769 5680; Passcode: 951510 ]

Abstract
Over the past decade, there has been a growing interest in evolution equations of parabolic type that involve fractional-order derivatives in time of order in (0, 1). Such equations, also called subdiffusion equations, arise in various applications in engineering, physics, biology and finance. Hence, it is quite important to develop efficient and reliable computational tools for their numerical solution.
In this talk, I will touch on similarities and differences between fractional-parabolic equations and their classical counterparts, including the non-local nature of fractional-order derivatives, initial-time solution singularities, and slower long-term solution decay, as well as the proofs of some regularity properties and maximum principles. Then we shall consider some robust numerical methods for such equations, as well as the derivation of a-priori and a-posteriori estimates of the computational errors.

Bio

Natalia Kopteva is a Full Professor at the Department of Mathematics and Statistics at the University of Limerick, Ireland, and also serves as the University of Limerick Research Integrity Officer and on the Ethics Committee of the European Mathematical Society.
She holds an M.Sc. in Applied Mathematics and a Ph.D. in Computational Mathematics, both from Moscow State University. In the past, she held academic positions at Moscow State University, University College Cork, and University of Strathclyde. She is associated with INAF - Irish Numerical Analysis Forum, MACSI - Mathematics Applications Consortium for Science and Industry, and the SFI Centre for Research Training in Foundations of Data Science.
Natalia’s research expertise lies in the area of Numerical Analysis for partial differential equations. She has authored a book chapter and 65 publications in international refereed journals, presented 13 plenary and more than 20 invited lectures at international meetings and conferences. She is editor for SIAM Journal on Numerical Analysis and Advances in Computational Mathematics, and, including her past editorial duties, has served as editor for 8 international refereed journals.

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