The suitability of pde‐solvers in rhizosphere modeling,exemplified by three mechanistic rhizosphere models

Mechanistic rhizosphere models are mathematical models that calculate the uptake of solutes (e.g. nutrients such as P or K) in a plant root and/or the concentration profiles of ions or microorganisms across the rhizosphere. They consist of partial differential equations (pde's) and their associated initial and boundary conditions, and often require numerical solutions due to non‐linearity. The suitability of the pde‐solver FlexPDE for rhizosphere modeling was evaluated by reproducing the outputs of three original rhizosphere models and comparing the results with the original model outputs. The models considered were NST 3.0 (Syring and Claassen, 1996), Kirk (1999), and Newman and Watson (1977). From visual comparison, the curves as produced by the original model and FlexPDE match very well. All calculated R²s (coefficients of determination) were equal to 1 with a rounding precision of three decimal places. Rescaling the time, using an upwind scheme in the presence of convection terms and controlling the relative error with the FlexPDE function errlimit were helpful in finding the most accurate numerical solution. These results showed that FlexPDE is a valuable tool in rhizosphere modeling.