Abstract. The paper presents the results in the construction of highly accurate computational algorithms for the classes of partial derivative problems with discontinuous solutions, including conditionally well-posed and eigenvalue problems. The optimal control in complex distributed systems is investigated. On the basis of the optimal control theory, explicit expressions are obtained for gradients of residual functionals to identify different parameters of multicomponent distributed systems. The possibility of using pseudoinverse matrices to solve some linear inverse problems in a finite number of arithmetic operations is considered.

Keywords: multicomponent distributed systems, numerical modeling, optimal control, parameter identification.