  In this study, we derive an analytical solution to address the problem of
one-dimensional vertical infiltration within bounded profiles. We consider the
Richards equation together with various boundary conditions, simulating
different scenarios of water application onto the surface of a homogeneous and
bounded medium. To solve the corresponding initial boundary value problem over
a finite interval, we apply the unified transform, commonly known as the Fokas
method. Through this methodology, we obtain an integral representation that can
be efficiently and directly computed numerically, yielding a convergent scheme.
