Numerical Solution to One Problem of Optimal Control of Technological Operating Models of Gas Wells to Prevent Pollution

In the paper, we consider the numerical solution to an optimal control problem related to technological operating models of gas wells. The process is described by nonlinear boundary value problems of parabolic type concerning matching conditions in the area of the bottom-hole zone of the formation. The numerical solution of the problem under consideration is based on the approximation of partial equations by ordinary differential equations. The numerical solution of the variational problem related to ordinary differential equations is based on the Pontryagin maximum principle. An algorithm for a numerical solution to the problem under consideration is proposed, and based on this algorithm, the implementation code is created. In this case, the Cauchy problem for the initial and conjugate system is integrated by the Runge-Kutta method with a choice of a constant step.