(m, k)-Methods for Control Theory Problems

This paper deals with the derivation of numerical methods for optimal control problems. Many of these problems lead to the necessity of the differential-algebraic equations solution of index 1 and higher. The review of control theory problems is given. An L-stable non-iterative (3, 2)-method of order 2 for the Cauchy problem for systems of index not exceeding 2 is proposed. New approach requires 2 function evaluations, 1 computation of the Jacobian matrix and LU-matrix decomposition at each integration step. Numerical results confirming the efficiency of the method are given.