Runge-Kutta methods are stable
Numerical Analysis
2023-12-27 v1 Numerical Analysis
Functional Analysis
Abstract
We prove that Runge-Kutta (RK) methods for numerical integration of arbitrarily large systems of Ordinary Differential Equations are linearly stable. Standard stability arguments -- based on spectral analysis, resolvent condition or strong stability, fail to secure the stability of arbitrarily large RK systems. We explain the failure of different approaches, offer a new stability theory and demonstrate a few examples.
Cite
@article{arxiv.2312.15546,
title = {Runge-Kutta methods are stable},
author = {Eitan Tadmor},
journal= {arXiv preprint arXiv:2312.15546},
year = {2023}
}