The problem of electromagnetic waves scattering on the small particle is reduced to solving the Fredholm integral equation of the second kind. Integral representation of solutions to the diffraction problem implies in determination of some auxiliary function which contains in integrand of this equation. The respective linear algebraic system for the components of this auxiliary function is derived and solved by the successive approximation method. The region of convergence of the proposed method is substantiated numerically. The numerical results show rapid convergence in the wide region of the physical and geometrical parameters of problem. The numerical results of scattering on the particles of various forms and sizes are presented.
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