Cite this article as:
Khromov A. A. The Solution of a Certain Inverse Problem. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2016, vol. 16, iss. 2, pp. 180-183. DOI: https://doi.org/10.18500/1816-9791-2016-16-2-180-183
The Solution of a Certain Inverse Problem
The solution is given for the problem of findinging uniform approximations of a the right-hand side of a general linear ordinary differential equation in the case when approximations of the exact solution are known. The constructed method has a simple structure, produces approximations of the right-hand side on the whole interval of definition and does not employ boundary conditions.
1. Ivanov V. K., Vasin V. V., Tanana V. P. Teoriia lineinykh nekorrektnykh zadach i ee prilozheniia [The theory of linear ill-posed problems and its applications]. Moscow, Nauka, 1978, 206 p. (in Russian).
2. Denisov A. M. Vvedenie v teoriiu obratnykh zadach [Introduction to the theory of inverse problems]. Moscow, Moscow Univ. Press, 1994, 206 p. (in Russian).
3. Khromov A. A., Khromova G. V. The Solution of the Problem of Determining the Dendity of Heat Sources in a Rod. Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2015, vol. 15, iss. 3, pp. 309–314. DOI: https://doi.org/10.18500/1816-9791-2015-15-3-309-314 (in Russian).
4. Khromov A. A. Approximation of Function and Its Derivative by the Modificated Steklov Operator. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2014, vol. 14, iss. 4, pt. 2, pp. 593–597 (in Russian).
5. Khromov A. P., Khromova G. V. Discontinuous Steklov operators in the problem of uniform approximation of derivatives on closed integral. Comput. Math. Math. Phys., 2014, vol. 54, no. 9, pp. 1389–1394. DOI: https://doi.org/10.1134/S0965542514090085.
