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

Abstract

ABSTRACT 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.