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

Beyond the mesh handling Maxwell's curl equations with an unconditionally leapfrog stable scheme