  We consider a splitting approach for the Kadomtsev--Petviashvili equation
with periodic boundary conditions and show that the necessary interpolation
procedure can be efficiently implemented. The error made by this numerical
scheme is compared to exponential integrators which have been shown in Klein
and Roidot (SIAM J. Sci. Comput., 2011) to perform best for stiff solutions of
the Kadomtsev--Petviashvili equation. Since many classic high order splitting
methods do not perform well, we propose a stable extrapolation method in order
to construct an efficient numerical scheme of order four. In addition, the
conservation properties and the possibility of order reduction for certain
initial values for the numerical schemes under consideration is investigated.
