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Positively invariant cones of dynamical systems under Runge‐Kutta and Rosenbrock‐type discretization
Author(s) -
Horváth Zoltán
Publication year - 2004
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200410325
Subject(s) - discretization , monotonic function , runge–kutta methods , invariant (physics) , mathematics , generalization , type (biology) , simple (philosophy) , dynamical systems theory , mathematical analysis , differential equation , mathematical physics , physics , ecology , philosophy , epistemology , quantum mechanics , biology
In this paper we consider positively invariant cones of finite dimensional dynamical systems and study conditions on the time step‐size that guarantee the discrete positive invariance of these cones under Runge‐Kutta and Rosenbrock‐type methods. We conclude quite simple sufficient conditions, which involve the positivity (or absolute monotonicity) radius of the Runge‐Kutta schemes and its generalization when the Rosenbrock‐type methods are applied. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)