Applicability of the method of nets and the method of lines to the solution of a class of problems of optimal control theory

The control of elliptic systems with solutions in class $W_2^2$ is considered. By means of the operators of exact difference schemes, schemes are constructed for which rate of convergence estimates of order $O(|h|^2)$ are established. Similar results are obtained for schemes of the method of straight lines, for the control of parabolic systems.