Abstract
A method for solving the linear boundary value problem for an integro-differential equation is proposed that is based on interval partition and the introduction of additional parameters. Necessary and sufficient conditions for the solvability of the problem are obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
N. M. Krylov, “On Generalization of Rietz’s Least Squares Method for Numerical Integration of Equations in Mathematical Physics,” Tr. Fiz.-Mat. Viddilu Akad. Nauk USSR 3, 3–28 (1926).
V. I. Romanovskii, “On an Integro-Differential Equation,” Tr. SAGU, Ser. Mat., No. 12, 25–32 (1934).
A. I. Nekrasov, “On a Class of Linear Integro-Differential Equations,” Tr. Tsentr. Aerogidrodin. Inst., No. 190, 1–25 (1934).
Ya. V. Bykov, On Some Problems in the Theory of Integro-Differential Equations (Kirgiz. Gos. Univ., Frunze, 1957) [in Russian].
T. I. Vigranenko, “A Boundary Value Problem for Linear Integro-Differential Equations,” Zap. Leningr. Gorn. Inst. 33(3), 177–187 (1956).
L. E. Krivoshein, Approximate Methods for Solving Linear Ordinary Integro-Differential Equations (Akad. Nauk Kirg. SSR, Frunze, 1962) [in Russian].
A. M. Samoilenko, O. A. Boichuk, and S. A. Krivosheya, “Boundary Value Problems for Systems of Linear Integro-Differential Equations with Degenerate Kernel,” Ukr. Mat. Zh. 48, 1576–1579 (1996).
V. S. Sharoglazov and V. V. Vasil’ev, “A Method for Approximate Solution of Boundary Value Problems for Linear Integro-Differential Equations,” Differ. Integr. Uravn. Irkutsk 3, 212–217 (1975).
A. Zh. Artykov, “Solvability Conditions for the Boundary Value Problem for Integro-Differential Equations,” in Research on Integro-Differential Equations (Ilim, Bishkek, 1994), Vol. 25, pp. 110–113 [in Russian].
O. V. Fodchuk, “Variational Iterative Method for Solving Boundary Value Problems for Integro-Differential Equations,” in Research Methods for Differential and Functional Differential Equations (Akad. Nauk USSR, Kiev, 1990), pp. 101–109 [in Russian].
O. O. Kurbanbaev, “A Boundary Value Problem for Integro-Differential Equations,” in Boundary Value Problems in Mathematical Physics (Kiev, 1990), pp. 29–34 [in Russian].
Kh. Ob. Franko, “On a Class of Integro-Differential Equations,” Vestn. Ross. Univ. Druzhby Narodov, Ser. Prikl. Mat. Inf., No. 1, 134–139 (1999).
D. S. Dzhumabaev, “Conditions for Unique Solvability of a Linear Boundary Value Problem for an Ordinary Differential Equation,” Zh. Vychisl. Mat. Mat. Fiz. 29, 50–66 (1989).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © D.S. Dzhumabaev, 2010, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2010, Vol. 50, No. 7, pp. 1209–1221.
Rights and permissions
About this article
Cite this article
Dzhumabaev, D.S. A method for solving the linear boundary value problem for an integro-differential equation. Comput. Math. and Math. Phys. 50, 1150–1161 (2010). https://doi.org/10.1134/S0965542510070043
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0965542510070043