# Leaking Bucket Equation and Reversibility

Leaking Bucket Equation and Reversibility

How do reversible integrators work for nonreversible differential equations, such as the leaking bucket equation? This is investigated here for the asynchronous leapfrog integrator, a presumably novel variant of the well-known leapfrog method. For comparison, one can also choose the second-order nonreversible Runge–Kutta method, which is also known as Heun's method.

Both integrators empty the bucket only approximately, even in the long run. So the behavior of the reversed trajectories does not contradict the fact that any one-step method has a flat-line solution, given an autonomous rate function that is initially vanishing.