Runge-Kutta methods are stable

Eitan Tadmor

Runge-Kutta methods are stable

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arxiv 2312.15546 v1 pith:5PWGRJMS submitted 2023-12-24 math.NA cs.NAmath.FA

Eitan Tadmor This is my paper · ORCID

classification math.NAcs.NAmath.FA

keywords stabilityarbitrarilylargemethodsrunge-kuttastablesystemsanalysis

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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.

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