An improvement on the positivity results for 2-stage explicit Runge–Kutta methods

In this paper, we investigate the positivity property for a class of 2-stage explicit Runge–Kutta (RK2) methods of order two when applied to the numerical solution of special nonlinear initial value problems (IVPs) for ordinary differential equations (ODEs). We also pay particular attention to monotonicity property. We obtain new results for positivity which are important in practical applications. We provide some numerical examples to illustrate our results.