Semi-Implicit and Explicit Runge Kutta Methods for Stiff Ordinary Differential Equations

Abstract In this work, we study the A [ α ] – stability of the additive methods of Runge- Kutta kind of orders ranging from 2 up to 4 that will be applied for determining some stiff nonlinear system of the ODEs. Moreover, we find the stability function for the additive Runge-Kutta method and some methods of this type of order 2,3, and 4. Where the method ( A,B 1 ) is A-stable and semi-implicit and method ( A,B 2 ) is explicit. Furthermore, the stiff term is managed by the semi-implicit Runge-Kutta method while no stiff term is treated by the explicit Runge Kutta method. Those methods are suitable for solving chemical reactions problems that include stiff and non-stiff terms.