Forecasting water content dynamics in heterogeneous porous media has
significant interest in hydrological applications; in particular, the treatment
of infiltration when in presence of cracks and fractures can be accomplished
resorting to peridynamic theory, which allows a proper modeling of non
localities in space. In this framework, we make use of Chebyshev transform on
the diffusive component of the equation and then we integrate forward in time
using an explicit method. We prove that the proposed spectral numerical scheme
provides a solution converging to the unique solution in some appropriate
Sobolev space. We finally exemplify on several different soils, also
considering a sink term representing the root water uptake
