 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4760 |
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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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