Positivity of exponential Runge-Kutta methods
In this article, we study positivity properties of exponential Runge-Kutta methods for abstract evolution equations. Our problem class includes linear ordinary differential equations with a time-dependent inhomogeneity. We show that the order of a positive exponential Runge-Kutta method cannot exceed two. On the other hand there exist second-order methods that preserve positivity for linear problems. We give some examples for the latter.
exponential runge-kutta methods abstract evolution equations exponential quadrature methods positivity in abstract spaces