# APPLICATION OF THE COMPUTATIONAL ALGORITHM OF THE MATRIX SWEEP METHOD

## Авторы

• P.A. Kozhabekova M. Auezov South Kazakhstan University, Shymkent, Kazakhstan
• Z.A. Makhanova M. Auezov South Kazakhstan University, Shymkent, Kazakhstan
• S.K. Mamekova M. Auezov South Kazakhstan University, Shymkent, Kazakhstan
• S.N. Kurbanbayeva M. Auezov South Kazakhstan University, Shymkent, Kazakhstan
• V. Moroz National University "Lviv Polytechnic", Lviv, Ukraine

## Ключевые слова:

heat conduction equations, increased accuracy method, regularized problems, ill-posed problems, approximation, stability, matrix sweep method, stability method

## Аннотация

The solution of inverse problems of thermal conductivity with a high-precision scheme is carried out by the method of approximate selection in the given article.

However, they try to use internal inverse problems of thermal conductivity to simplify calculations, which leads them to specific analytical expressions that are independent of the thermal effect, temperature field, and geometry of the sample. The solution of inverse problems of thermal conductivity with a high-precision scheme is carried out by the method of approximate selection.

The high-precision method is considered with the crank-Nicholson type difference scheme in this article. The crank-Nicholson type scheme is a parabolic differential equation of finite difference.

In particular, the advantage of the difference scheme is that the solution in the upper time layer is obtained immediately according to the values of the grid function in the lower time layer and it is without the solution of the system of linear algebraic equations (Satz), and also in it the solution becomes known (at k = 0, the values of the grid function are formed from the initial situation). But the same scheme has a significant disadvantage, since it is conditionally stable. On the other hand, the fuzzy difference scheme leads to the need to solve the SATs of a system of linear algebraic equations, but this scheme is absolutely stable.

The solution of the inverse problem of thermal conductivity with a high-precision circuit is defined as the limit of the solution group.For example, a well-known calculation algorithm of the Matrix method is used to solve a three-point boundary problem, the parameters of which satisfy the stability condition. Since there are inverse matrices, the necessary conditions for the stability of the Matrix method are met.

2022-06-29

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