Positive and elementary stable explicit nonstandard Runge-Kutta methods for a class of autonomous dynamical systems

In this paper, we construct and analyze explicit nonstandard Runge-Kutta (ENRK) methods which have higher accuracy order and preserve two important properties of autonomous dynamical systems, namely, the positivity and linear stability. These methods are based on the classical explicit Runge-Kutta m...

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Bibliographic Details
Published in:International journal of computer mathematics 2020-10, Vol.97 (10), p.2036-2054
Main Authors: Dang, Quang A, Hoang, Manh Tuan
Format: Article
Language:English
Subjects:
37M
65L
65Q
autonomous dynamical systems
Computer simulation
Dynamic stability
Dynamical systems
elementary stable
Explicit Runge-Kutta methods
nonstandard finite difference schemes
Numerical methods
positive finite difference methods
Runge-Kutta method
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Summary:In this paper, we construct and analyze explicit nonstandard Runge-Kutta (ENRK) methods which have higher accuracy order and preserve two important properties of autonomous dynamical systems, namely, the positivity and linear stability. These methods are based on the classical explicit Runge-Kutta methods, where instead of the usual h in the formulas there stands an appropriately chosen function . It is proved that the constructed methods preserve the accuracy order of the original Runge-Kutta methods. Some performed numerical simulations confirm the validity of the obtained theoretical results as well as the effectiveness of the proposed method.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207160.2019.1677895