Application of the method of straight lines to determining the stressed-strained state and dynamic characteristics of a hollow noncircular cylinder

1995 ◽  
Vol 75 (4) ◽  
pp. 1843-1848
Author(s):  
G. G. Vlaikov ◽  
O. Ya. Grigorenko ◽  
S. M. Shevchenko
Keyword(s):  
Dynamic Characteristics ◽  
Strained State ◽  
Noncircular Cylinder ◽  
Method Of Straight Lines ◽  
Straight Lines

Solution of Stefan's problem by the method of straight lines

1969 ◽  
Vol 9 (3) ◽  
pp. 113-126 ◽  
Author(s):  
R.D. Bachelis ◽  
V.G. Melamed ◽  
D.B. Shlyaifer
Keyword(s):  
Method Of Straight Lines ◽  
Straight Lines

scholarly journals Analysis of one class of optimal control problems for distributed-parameter systems

2021 ◽  
Vol 5 (4 (113)) ◽  
pp. 26-33
Author(s):  
Kamil Mamtiyev ◽  
Tarana Aliyeva ◽  
Ulviyya Rzayeva
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Optimal Control ◽  
Approximate Solution ◽  
Boundary Conditions ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Method Of Straight Lines ◽  
The Right ◽  
Straight Lines

In the paper, the method of straight lines approximately solves one class of optimal control problems for systems, the behavior of which is described by a nonlinear equation of parabolic type and a set of ordinary differential equations. Control is carried out using distributed and lumped parameters. Distributed control is included in the partial differential equation, and lumped controls are contained both in the boundary conditions and in the right-hand side of the ordinary differential equation. The convergence of the solutions of the approximating boundary value problem to the solution of the original one is proved when the step of the grid of straight lines tends to zero, and on the basis of this fact, the convergence of the approximate solution of the approximating optimal problem with respect to the functional is established. A constructive scheme for constructing an optimal control by a minimizing sequence of controls is proposed. The control of the process in the approximate solution of a class of optimization problems is carried out on the basis of the Pontryagin maximum principle using the method of straight lines. For the numerical solution of the problem, a gradient projection scheme with a special choice of step is used, this gives a converging sequence in the control space. The numerical solution of one variational problem of the mentioned type related to a one-dimensional heat conduction equation with boundary conditions of the second kind is presented. An inequality-type constraint is imposed on the control function entering the right-hand side of the ordinary differential equation. The numerical results obtained on the basis of the compiled computer program are presented in the form of tables and figures. The described numerical method gives a sufficiently accurate solution in a short time and does not show a tendency to «dispersion». With an increase in the number of iterations, the value of the functional monotonically tends to zero

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