  Numerical solution of equations governing time domain simulations in
computational electromagnetics, is usually based on grid methods in space and
on explicit schemes for the time evolution. A predefined grid in the problem
domain and a stability step size restriction must be accepted. Evidence is
given that efforts need for overcoming these heavy constraints. Recently, the
authors developed a meshless method to avoid the connective laws among the
points scattered in the problem domain. Despite the good spatial properties,
the numerical explicit integration used in the original formulation of the
method provides,also in a meshless context, spatial and time discretization
strictly interleaved and mutually conditioned. Afterwards, in this paper the
stability condition is firstly addressed in a general way by allowing the time
step increment get away from the minimum points spacing. Meanwhile, a
formulation of the alternating direction implicit scheme for the evolution in
time is combined with the meshless solver. The formulation preserves the
leapfrog marching on in time of the explicit integration scheme. The new
method, not constrained by a gridding in space and unconditionally stable in
time, is numerical assessed by different numerical simulations. Perfect
matching layer technique is used in simulating open spatial problems;
otherwise, a consistency restoring approach is introduced in treating
truncation at finite boundary and irregular points distribution. Three case
studies are investigated by achieving a satisfactory agreement comparing both
numerical and analytical results.
