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A Journal of Russian Academy of Sciences
 Founded
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IssuesArchive of Issues2003-2pp.122-127

Archive of Issues

Total articles in the database: 11223
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8011
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A. Yu.Vinogradov, Yu. I. Vinogradov, Yu. A. Gusev, and Yu. I. Klyuev, "A method for solving a two-point boundary value problem based on Cauchy-Krylov functions," Mech. Solids. 38 (2), 122-127 (2003)
Year 2003 Volume 38 Number 2 Pages 122-127
Title A method for solving a two-point boundary value problem based on Cauchy-Krylov functions
Author(s) A. Yu.Vinogradov (Moscow)
Yu. I. Vinogradov (Moscow)
Yu. A. Gusev (Moscow)
Yu. I. Klyuev (Moscow)
Abstract The problem of transferring boundary conditions of linear ordinary differential equations of the theory of shells connected with the instability of computer calculations has been approached in various ways in the framework of the Abramov, Gel'fand-Lokutsievskii, and Godunov methods. A common essential feature of these methods is the numerical integration of differential equations with standard types of boundary conditions by Runge-Kutta methods of various orders. Numerical integration of these differential equations progressing from one end-point of the interval or from both ends simultaneously allows one to construct a system of algebraic equations at an arbitrary point of the integration interval and thereby solve the problem. The essential distinctive features of the proposed method involve the analytical calculation of the values of the Krylov functions for linear ordinary differential equations, independently of the boundary conditions and the transfer of these conditions by means of recurrent relations constructed on the basis of the properties of the Cauchy-Krylov functions.
References
1.  F. R. Gantmakher, Theory of Matrices [in Russian], Nauka, Moscow, 1966.
2.  A. N. Krylov, The Design of Beams on an Elastic Base [in Russian], Izd-vo AN SSSR, Leningrad, 1931.
3.  A. Yu. Vinogradov and Yu. I. Vinogradov, "A method of transferring boundary conditions by the Cauchy-Krylov functions for stiff linear ordinary differential equations," Doklady AN, Vol. 373, No. 4, pp. 474-476, 2000.
4.  S. K. Godunov, "On the numerical solution of boundary value problems for systems of linear ordinary differential equations," Uspekhi Matem. Nauk, Vol. 16, No. 3, pp. 171-174, 1961.
Received 24 April 2001
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