Solving the Master Equation on river networks: A computer algebra approach

Abstract

We describe the algorithms and the software that have been used in a new computational method based on the use of Master Equations. Our computer algebra procedures simulate the diffusion of a pollutant in river networks. The representation of river networks as trees makes the derivation of governing equations for pollutant transport an easy task. This includes mass balance equations that account for the sources, sinks, and transport of pollutants in the river network. In two previous papers we described the model and some simulations obtained from our software. In this paper we describe two software libraries, respectively for the Reduce and the Mathematica computer algebra systems, that have been developed on the basis of our model. The libraries can be found in our GitHub repository.