## Scientific Bulletin of Namangan State University

#### Article Title

#### Abstract

In this paper, we develop a method and algorithm for solving the problem of the optimal selection of the density o f heat sources on the rod in such a way that the temperature inside the considered region is within the given limits. At the same time, heat sources must provide a given temperature regime o f the minimum total power and temperature in a given corridor. Conservative approximations o f the original problem are constructed in the form o f a linear programming problem. A method for constructing conservative schemes for solving the heat equation with variable coefficients, a brief description o f the developed software application for constructing computational grids and solving equations is given. A new method is proposed and justified for the numerical solution of non-stationary problems of the optimal selection of heat sources in the rod. A software application for conducting numerical experiments to solve the problem has been created. A description of the based algorithm and the results of numerical experiments is provided

#### First Page

26

#### Last Page

38

#### References

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#### Erratum

???????

#### Recommended Citation

Tukhtasinov, Muminjon and Khayitkulov, Bobomurod Khayitovich
(2020)
"CONSERVATIVE SCHEMES OF THE NON-STATIONARY PROBLEM FOR THE
OPTIMAL SELECTION OF THE LOCATION OF HEAT SOURCES IN THE ROD,"
*Scientific Bulletin of Namangan State University*: Vol. 2
:
Iss.
9
, Article 5.

Available at:
https://uzjournals.edu.uz/namdu/vol2/iss9/5