Abstract
Abstract The inverse problem with identification parameter for system of ordinary differential equations is considered. Definition of the isolated solution for the inverse problem with identification parameter to nonlinear system of ordinary differential equations is introduced. For finding of the isolated solution to problem is used the parametrization method. The method consists in partitioning of the considered interval, introducing of parameters and reducing the original problem to the equivalent multi-point identification parameter problem. The algorithms for finding an approximate solution to the equivalent problem are offered. Each step of the algorithm consists of two stages: a) solving of the nonlinear system of equations with respect to the parameters, composed by the initial data of the problem, and b) solving the Cauchy problems on corresponding intervals at the founded parameters values. The conditions for convergence of the algorithms that ensure the solvability of the inverse problem with identification parameter are established. The necessary and sufficient conditions for the existence of the isolated solution to the inverse problem with identification parameter are obtained in the terms of the right-hand side of the system of differential equations and the boundary conditions.