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Runge–Kutta Methods for Monotone Differential and Delay Equations

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2003

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Kloeden, Peter E.

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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.

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Fachgebiet (DDC)
510 Mathematik

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monotone dynamical systems, delay equations, Runge–Kutta methods

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ISO 690KLOEDEN, 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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