Runge–Kutta Methods for Monotone Differential and Delay Equations
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| Type of Publication: | Journal article |
| Publication status: | Published |
| Author: | Kloeden, Peter E.; Schropp, Johannes |
| Year of publication: | 2003 |
| Published in: | BIT - Numerical Mathematics ; 43 (2003), 3. - pp. 571-586. - ISSN 0006-3835. - eISSN 1572-9125 |
| DOI (citable link): | https://dx.doi.org/10.1023/B:BITN.0000007059.99601.18 |
| Summary: |
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.
|
| Subject (DDC): | 510 Mathematics |
| Keywords: | monotone dynamical systems, delay equations, Runge–Kutta methods |
| Bibliography of Konstanz: | Yes |
| Refereed: | Unknown |
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KLOEDEN, Peter E., Johannes SCHROPP, 2003. Runge–Kutta Methods for Monotone Differential and Delay Equations. In: BIT - Numerical Mathematics. 43(3), pp. 571-586. ISSN 0006-3835. eISSN 1572-9125. Available under: doi: 10.1023/B:BITN.0000007059.99601.18
@article{Kloeden2003-09Runge-43197, title={Runge–Kutta Methods for Monotone Differential and Delay Equations}, year={2003}, doi={10.1023/B:BITN.0000007059.99601.18}, 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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