Solving partial differential equations, using R package ReacTran

R -package ReacTran (Soetaert and Meysman 2009) contains functions to solve reactivetransport equations, as used e.g. in the environmental sciences. Essentially, it 1. Provides functions that subdivide the spatial extent into a number of discrete grid cells. 2. Approximates the advective-diffusive transport term by finite differences or finite volumes. The main package vignette (Soetaert and Meysman 2010) explains how ReacTran can be used to model reaction-transport phenomena. However, the functions from ReacTran can be use to solve more general types of partial differential equations (≤ order 2). In this vignette, show how the package can be used to solve partial differential equations of the parabolic, hyperbolic and elliptic type, providing one example each.