SINOPSIS

An approach to numerical solution of the coefficient inverse problems with respect to systems of linear non-autonomous differential equations with ordinary derivatives is proposed. The observations of various kinds are used to identify the coefficients. The approach uses a special transform of the solution of a boundary-value problem relative to the initial linear system of differential equations with nonlocal conditions. The use of this approach enables one to reduce the parametric identification problem to solving the auxiliary boundary value problems with nonlocal conditions and one system of algebraic equations. The approach can be used to solve the coefficient inverse problems, described by partial differential equations, in which the identified coefficients depend only on one variable: time or spatial. Numerical results and their analysis are given.