Special Lecture - 2/22, 12:00PM, Duncan Hall 1049

David Ketcheson

Department of Applied Mathematics and Computational Science
King Abdullah University of Science and Technology

"Better Numerical Methods for Time-Discretization of PDEs"

Many important phenomena are modelled by time-dependent partial differential equations whose accurate solution is challenging and costly. Numerical algorithms for these problems must satisfy particular stability and accuracy constraints while marching as rapidly as possible. I will introduce some examples of valuable but costly time-dependent wave equation computations. Then I will give an introduction to key stability concepts in time discretization of PDEs, followed by a description of my recent work aimed at answering questions like:

• How can we design accurate, stable numerical methods that march faster in time?
• Can we find methods that ensure positivity of solutions?
• What are the theoretical limits on achievable efficiency of time discretizations for PDEs?