Runge–Kutta Methods for Monotone Differential and Delay Equations

Kloeden, Peter E.; Schropp, Johannes

Runge–Kutta Methods for Monotone Differential and Delay Equations

Dateien

Zu diesem Dokument gibt es keine Dateien.

Datum

2003

Autor:innen

Kloeden, Peter E.

Schropp, Johannes

DOI (zitierfähiger Link)

https://doi.org/10.1023/B:BITN.0000007059.99601.18

Sammlungen

Mathematik und Statistik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

BIT - Numerical Mathematics. 2003, 43(3), pp. 571-586. ISSN 0006-3835. eISSN 1572-9125. Available under: doi: 10.1023/B:BITN.0000007059.99601.18

Zusammenfassung

Classes of Runge–Kutta methods preserving the monotonicity of ordinary and delay differential equations are identified. Essentially, the vector b and the matrix A from the Butcher tableau should be such that all components of b are positive and all components of the matrix B(r)A, where B(r) is the inverse of the matrix I+rA, are nonnegative for sufficiently small positive r. The latter is satisfied by all explicit, diagonally-implicit and fully implicit Runge–Kutta methods for which all of the components of the matrix A, except those that are zero by definition, are positive.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

monotone dynamical systems, delay equations, Runge–Kutta methods

Zitieren

ISO 690

KLOEDEN, Peter E., Johannes SCHROPP, 2003. Runge–Kutta Methods for Monotone Differential and Delay Equations. In: BIT - Numerical Mathematics. 2003, 43(3), pp. 571-586. ISSN 0006-3835. eISSN 1572-9125. Available under: doi: 10.1023/B:BITN.0000007059.99601.18

BibTex

@article{Kloeden2003-09Runge-43197,
  year={2003},
  doi={10.1023/B:BITN.0000007059.99601.18},
  title={Runge–Kutta Methods for Monotone Differential and Delay Equations},
  number={3},
  volume={43},
  issn={0006-3835},
  journal={BIT - Numerical Mathematics},
  pages={571--586},
  author={Kloeden, Peter E. and Schropp, Johannes}
}

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