The positive projection method presented in the paper ensures mass conservation and positivity. First, a numerical approximation is computed with one step of a mass-preserving traditional scheme. If there are negative components the nearest vector in the reaction simplex is found using a primal-dual optimization routine; this vector is shown to better approximate the true solution. A simpler version involves just one projection step and stabilizes the reaction simplex.
The techniques works best when the underlying time-stepping scheme favors positivity. Projected methods are able to use larger integration time steps, being more efficient then traditional methods for systems which are unstable outside the positive quadrant.