Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)3510810.22363/2658-4670-2023-31-2-120-127WIMGRXArticlesСтатьиResearch ArticleConvergence of the grid method for the Fredholm equation of the first kind with Tikhonov regularizationСходимость сеточного метода для уравнения Фредгольма первого рода с регуляризацией по Тихоновуhttps://orcid.org/0000-0002-0918-926357191950560Q-5064-2016BelovAleksandr A.БеловА. А.

Candidate of Physical and Mathematical Sciences, Researcher of Faculty of Physics, M. V. Lomonosov Moscow State University; Assistant Professor of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia

aa.belov@physics.msu.ruM. V. Lomonosov Moscow State UniversityМосковский государственный университет им. М. В. ЛомоносоваRUDN UniversityРоссийский университет дружбы народов30062023312VOL 31, NO2 (2023)ТОМ 31, №2 (2023)12012729062023Copyright ©; 2023, Belov A.A.Copyright ©; 2023, Белов А.А.2023Belov A.A.Белов А.А.https://creativecommons.org/licenses/by-nc/4.0https://journals.rudn.ru/miph/article/view/35108

The paper describes a grid method for solving an ill-posed problem for the Fredholm equation of the first kind using the A. N. Tikhonov regularizer. The convergence theorem for this method was formulated and proved. A procedure for thickening grids with a simultaneous increase in digit capacity of calculations is proposed.

В статье описан сеточный метод решения некорректной задачи для уравнения Фредгольма первого рода с использованием регуляризатора А. Н. Тихонова. Сформулирована и доказана теорема о сходимости этого метода. Для её практической реализации предложена процедура сгущения сеток с одновременным увеличением разрядности вычислений.

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