Publikation: 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.
Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
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monotone dynamical systems, delay equations, Runge–Kutta methods
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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.0000007059.99601.18BibTex
@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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