Runge-Kutta methods for monotone differential and delay equations (Q1431664)

The authors present classes of Runge-Kutta methods for nonlinear ordinary and delay differential equations for which the numerical dynamical system shares the monotonicity behaviour of the continuous time system. A Runge-Kutta method is given by the weight vector and the coefficient matrix \(A\). The positivity of the weights and the nonnegativity of the components of the matrix \((I+\tau A)^{-1}A\) for sufficiently small \(\tau>0\) ensure that the monotonicity is preserved.