On Abstract Spectral Constants

Schwenninger, Felix L.; de Vries, Jens

doi:10.1007/978-3-031-50613-0_15

Operator Theory: Advances and Applications

2024

DOI: 10.1007/978-3-031-50613-0_15

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On Abstract Spectral Constants

Felix L. Schwenninger,

Jens de Vries

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On the stability of Runge–Kutta methods for arbitrarily large systems of ODEs

Tadmor

2024

Comm Pure Appl Math

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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 RK methods for arbitrarily large systems. We explain the failure of different approaches, offer a new stability theory based on the numerical range of the underlying large matrices involved in such systems, and demonstrate its application with concrete examples of RK stability for hyperbolic methods of lines.

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On the stability of Runge–Kutta methods for arbitrarily large systems of ODEs

Tadmor

2024

Comm Pure Appl Math

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show abstract

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On Abstract Spectral Constants

Cited by 1 publication

References 21 publications

On the stability of Runge–Kutta methods for arbitrarily large systems of ODEs

On the stability of Runge–Kutta methods for arbitrarily large systems of ODEs

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