Certain numerical methods of developing an optimal plan of economy. Evolution. II. Solving the Cauchy problem for a system of differential! equations generated by the linear optimization problem

The paper is an extension of Ref. [1]. The Cauchy problem is considered for a system of linear differential equations with a control which is found from solution to the linear programming (LP) problem whose parameters depend on the system phase coordinates. Such systems are encountered in working out an optimal economic plan. A method is proposed in which the LP problem is solved in system integration by finite formulae everywhere except the initial point of the trajectory in the Cauchy problem. The method is also applicable to the case where the system of differential equations is nonlinear.