A comparison of numerical methods for conservative and positive advection‐diffusion‐production‐destruction systems

In many simulations it is important to guarantee positivity of the numerical approximations. For standard ODE solvers positivity is usually achieved by restrictions of the time step size, in contrast, MPRK schemes are unconditionally positive, which allows for much faster computations. We compare MPRK schemes and standard ODE solvers applied to an advection‐diffusion‐produ system for which it is essential to avoid negative approximations .