In the report we present a new pollution-free approach to the finite difference reduced-order numerical solving of the wave propagation problem in an axisymmetrical open trap. This approach makes it possible to use an arbitrary mesh. This possibility is very important for ICRF modeling since it allows one to construct a mesh whose lines are aligned along the steady magnetic field and the density of mesh nodes reflects the structure of cyclotron zones in plasma column. In this approach the spurious branch of oscillations is removed and the distortion of numerical solutions in the near-axis region is suppressed. Basing on the approach proposed, a new version of the earlier developed PLFEM code, PLFEM-S, has been constructed. The results of the PLFEM-S code tests for stability and the first results are presented.