On Numerical Solution of Vector Wave Equations

The choice of wave equations as basic for the plasmas self-consistent potentials description is determined by their properties under rotations of coordinates. The algorithm of the numerical solving makes use of the differential operators invariance properties. The solution is expressed as a series in irreducible representations. Three-dimensional wave equations are reduced to the set of 2-D equations for amplitudes of the vector axial harmonics when the region has the axis of symmetry. In the case of the spherical region, 3-D vector wave equations are reduced to the set of 1-D equations for amplitudes of the vector spherical harmonics that are the irreducible representations of the rotation group. Finite-difference equations are obtained in the orthogonal curvilinear coordinates. It is shown that finite-difference schemes are stable in the energetic norm when the irreducible representations are used.