Comparison of numerical algorithms based on elementary and Muller's boundary integral equations in the scattering by dielectric cylinders

We consider boundary integral equations (BIEs) met in the scattering by dielectric cylinders and compare numerical algorithms based on elementary and Muller's BIEs near the "numerical resonances". A procedure of partial removal of well-known defect of elementary BIEs related to the loss of their unique solvability is discussed.