Numerical study of paraxial beam formation

A method for numerical study of different integral problems with sufficiently strongly localized solutions is considered. Approximations of the solution with different degrees of accuracy were constructed and, using the existing approximation, an approach to an increase of the solution accuracy is proposed. Numerical solutions are obtained for the problem of free oscillations of laser cavities the optical surface of which was approximated by polynomials of the second and fourth degree inclusive. The obtained numerical solutions were stable.