The energy technique for BDF methods
Prof. Georgios Akrivis
University of Ioannina

The energy technique (or method) is probably the easiest way to establish stability of parabolic (and other) differential equations.
The application of the energy technique to numerical methods with very good stability properties, such as algebraically stable Runge-Kutta methods or A-stable multistep methods, is straightforward. The extension to other numerical methods, such as A($\vartheta$)-stable methods, requires some effort and is more interesting; the main difficulty concerns suitable choices of  test functions.
Here we focus on the energy technique for backward difference formula (BDF) methods. In the cases of the A-stable one- and two-step BDF methods the application is trivial. The energy technique is applicable also to the A($\vartheta$)-stable three-, four- and five-step BDF methods via Nevanlinna-Odeh multipliers. 
The main results are:
No  Nevanlinna-Odeh multipliers exist for the six-step BDF method.
The energy technique is applicable under a relaxed condition on the multipliers.
We present multipliers that make the energy technique applicable also to the six-step BDF method.
The talk is based on the paper: G. Akrivis, M. Chen, F. Yu, Z. Zhou: The energy technique for the six-step BDF method, SINUM J. Numer. Anal. 59 (2021), 2449-2472. 

About the Speaker

Professor Georgios Akrivis is a Full Professor at Department of Computer Science and Engineering, University of Ioannina, Greece. Professor Akrivis received PhD degree from University of Munich, Germany. He was an Assistant and Associate Professor at University of Crete, and he moved to University of Ioannina as Full Professor in 1995. Professor Akrivis’ research interests include the numerical solution and analysis of linear and nonlinear evolutionary partial differential equations. He has published over 50 papers in journals like SIAM J. Numerical Analysis, Numerische Mathematik, and Mathematics of Computation. He is currently an Associate Editor of SIAM Journal on Numerical Analysis. 

2021-10-15 2:00 PM
Room: Zoom
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