ИНТЕГРО-ДИФФЕРЕНЦИАЛДЫҚ ТЕҢДЕУ ҮШІН ШЕТТІК ЕСЕПТІҢ БІРМӘНДІ ШЕШІМДІЛІГІН АЛУДЫҢ БІР ӘДІСІ ТУРАЛЫ

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Авторлар

  • К.Назарова

Аңдатпа

The modified method of parametrization is used to study a linear Fredholm integro-differential equation with a degenerate kernel. Using the fundamental matrix, the conditions are established for the existence of a solution to the special Cauchy problem for the Fredholm integro-differential equation with a degenerate kernel. A system of linear algebraic equations is constructed with respect to the introduced additional parameters. Conditions for the unique solvability of a linear boundary value problem for the Fredholm integro-differential equation with a degenerate kernel are obtained.

Әдебиеттер тізімі

Tomson J. Application of dynamics to physics and chemistry, London and New York, 1888

Ferle L. Kriticheskie chisla oborotov rotora opredelennoj formy s uchetom giroskopicheskogo effekta// Mekhanika. Period.sb.perevodov inostr. Statej. M.1956.№ 6(40), S.135-139.

Klöppel H.Lie, Lotrechte Swingungen von Hangebrücken, Ing. –Arch., 13, 1942.ss.211-266.

Gardner M., Berns D. Perekhodnye processy v linejnyh sistemah. GITTL. Moskva. 1951.

Vypov G.P. Nestacionarnoe dvizhenie vyazkoj neszhimaemoj zhidkosti mezhdu blizko raspolozhennymi dvizhushchimisya poverhnostyami. Izv. VUZov. № 3. 1958. S.1-49.

Bykov YA.V. O nekotoryh zadachah teorii integro-differencial'nyh uravnenij.-Frunze: Kirgiz.gos.universitet, 1957.

A.A. Boichuk, A.M. Samoilenko, Generalized inverse operators and Fredholm boundary-value problems, VSP, Utrecht, Boston, 2004.

H. Brunner, Collocation Methods for Volterra Integral and Related Functional Equations. Cambridge University, Press. 2004.

H. Du, G. Zhao, Ch. Zhao, Reproducing kernel method for solving Fredholm integro-differential equations with weakly singularity. J. Comput. Appl. Math. 255 (2014), pp. 122-132.

A.Iserles, Y.Liu, On pantograph integro-differential equations. Journal of Integral Equations and Applications. 6, (1994), pp. 213-237.

D.S. Dzhumabaev, A Method for Solving the Linear Boundary Value Problem for an Integro-Differential Equation. Comput. Math. Math. Phys. 50 (2010), pp. 1150-1161.

D.S. Dzhumabaev, Necessary and Sufficient Conditions for the Solvability of Linear Boundary-value Problems for the Fredholm Integro-Differential Equation. Ukr.Math.J. 66 (2015), pp. 1200-1219.

D.S. Dzhumabaev, On one approach to solve the linear boundary value problems for Fredholm integro-differential equations. Journal of Computational and Applied Mathematics. 294(2016), pp. 342-357.

D. S. Dzhumabaev, K.Zh.Nazarova, and R. E. Uteshova, A Modification of the Parameterization Method for a Linear Boundary Value Problem for a Fredholm Integro-Differential Equation

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2022-06-30