Runge–Kutta Methods for Monotone Differential and Delay Equations |
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Authors: | P E Kloeden J Schropp |
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Institution: | (1) Department of Mathematics, Johann Wolfgang Goethe University Frankfurt, 60054 Frankfurt am Main, Germany;(2) Department of Mathematics, University of Köln, 50931 Köln, Germany |
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Abstract: | 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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Keywords: | monotone dynamical systems delay equations Runge– Kutta methods |
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