Using the spheroidal coordinates for solving the diffraction problems by pattern equation method

In the present paper we used a prolate spheroidal coordinates in Pattern Equation Method for the numerical simulation of wave scattering by strongly elongated scatterer. We discuss the convergence and stability of numerical algorithms based on Pattern Equation Method. The calculations accuracy was controlled by means of calculating the balance of energy flows for the incident and scattered waves (verification of the "optical theorem"). It is shown that this method has high speed and universality.