For citation:
Khromov A. A., Khromova G. V. The Solution of the Problem of Determining the Density of Heat Sources in a Rod. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2015, vol. 15, iss. 3, pp. 309-314. DOI: 10.18500/1816-9791-2015-15-3-309-314, EDN: UKIVFZ
The Solution of the Problem of Determining the Density of Heat Sources in a Rod
We give a solution of a problem of determining the density of heat sources in the bav, which is set to a fixed temperature, if the temperature is given approximately. Mathematically it is the problem of finding uniform approximations to the right-hand side of the ordinary differential equation when uniform approximations to the solution and values of error are known. First using the so-called discontinuous Steklov operator we construct families of operators which give stable uniform approximations to a function and its first and second derivatives, and then with their help we propose the method of solving the formulated problem. For a certain class of solutions error estimations are given.
- Иванов В. К., Васин В. В., Танана В. П. Теория линейных некорректных задач и её приложения. М. : Наука, 1978. 206 с.
- Денисов А. М. Введение в теорию обратных задач. М. : Изд-во Моск. ун-та, 1994. 206 с.
- Хромов А. А. Приближение функции и её производных с помощью модифицированных операторов Стеклова // Изв. Сарат. ун-та. Нов. сер. Сер. Математика. Механика. Информатика. 2014. Т. 14, вып. 4, ч. 2. С. 593–597.
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