Volume 10, Issue 5

- In this paper we present formulas for solutions and coefficients of kinetic equations. The formulas contain arbitrary functions whose research in inverse problems for kinetic equations in a number of cases deals with conversion of the Hilbert, Fourier and Abel transforms, analytical continuation and other relations.

- A novel numerical method for solving inverse scattering problem with fixed-energy data is proposed. The method contains a new important concept: the stability index of the inversion problem. This is a number, computed from the data, which shows how stable the inversion is. If this index is small, then the inversion provides a set of potentials which differ so little, that practically one can represent this set by one potential. If this index is larger than some threshold, then practically one concludes that with the given data the inversion is unstable and the potential cannot be identified uniquely from the data. Inversion of the fixed-energy phase shifts for several model potentials is considered. The results show practical efficiency of the proposed method. The method is of general nature and is applicable to a very wide variety of the inverse problems.

- This paper is devoted to numerical analysis of ill-posed problems of evolution equations in Banach spaces. Since a C -semigroup is a regularizator family for an ill posed-problem we consider approximation by C -semigroups for a general approximation scheme. In this direction the relevant notion is that of C operator, which provides the regularization property. Within this context some interesting aspects of regularization using stochastic differential equations with discretization in space and in time variables are considered.