Keywords and phrases: regularization method (RM), small parameter, special solution, ill‑posed problem, system of the first kind Volterra integral equations (SVIE-1).
Received: February 25, 2022; Revised: March 30, 2022; Accepted: April 2, 2022; Published: May 10, 2022
How to cite this article: T. D. Omurov and A. M. Alybaev, Regularization of a system of the first kind Volterra incorrect two-dimensional equations, Advances in Differential Equations and Control Processes 27 (2022), 149-162. http://dx.doi.org/10.17654/0974324322018
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References:
[1] A. S. Apartsin, Non-classical Volterra equations of the 1st kind: theory and numerical methods, Novosibirsk, Science, 1999, p. 199. [2] D. S. Anikonov, On the question of the uniqueness of the solution of inverse problems for equations of mathematical physics, Differ. Equations 1 (1979), 3-9. [3] A. L. Bukhgeim, Volterra equation and inverse problems, Novosibirsk, Science, 1983, p. 207. [4] A. M. Denisov, On the approximate solution of the Volterra equation of the first kind associated with one inverse problem for the heat equation, West Moscow State University, Vychisl. Mat. and Cybern. 3 (1980), 49-52. [5] M. I. Imanaliev, Generalized solutions of integral equations of the first kind, Frunze, Ilim, 1981, p. 144. [6] M. M. Lavrent’ev, Integral equations of the first kind, Report of the Academy of Sciences of the USSR 127(1) (1959), 31-33. [7] T. D. Omurov, Regularization methods for Volterra integral equations of the first and third kind, Bishkek, Ilim, 2003, p. 162. [8] V. O. Sergeev, Regularization of the first kind Volterra equations, DAN SSSR 197(3) (1971), 531-534. [9] A. N. Tychonov and V. Y. Arsenin, Methods for Solving Ill-posed Problems, Nauka, 1986, p. 287. [10] Ten Myung Yang, Approximate solution of the first kind Volterra two-dimensional integral equations by the quadrature method, Differential and Integral Equations 3 (1975), 194-211.
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