@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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    <dc:contributor>Kloeden, Peter E.</dc:contributor>
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    <dcterms:abstract xml:lang="eng">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.</dcterms:abstract>
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    <dcterms:title>Runge–Kutta Methods for Monotone Differential and Delay Equations</dcterms:title>
    <dc:contributor>Schropp, Johannes</dc:contributor>
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