Lecture in the framework of the School of Mathematical Sciences’ colloquium: "Runge-Kutta methods are stable"

Professor Eitan Tadmor is a ​2024/2025 Lowy Distinguished Guest Professor of The Institute of Advanced Studies.

Abstract:

Runge-Kutta (RK) methods form a widely used class of discrete methods for numerical integration of systems of Ordinary Differential Equations (ODEs). In particular, RK methods are routinely used as ODE solvers of increasingly large systems encountered in various applications. But the standard stability arguments of RK methods fail to cover arbitrarily large systems.
 

We explain the failure of different approaches, offer a new stability theory and demonstrate a few examples.