Abstract
This paper is a direct continuation of [1]: it presents and analyzes the iterative variable direction method for the solution of the difference scheme approximating the first boundary-value problem plane elasticity theory on a polar grid.
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Literature cited
M. M. Karchevskii and S. N. Voloshanovskaya, “On approximation of the strain tensor in curvilinear coordinates. A difference scheme for the equilibrium problem of an elastic cylinder,” Izv. Vyssh. Uchebn. Zaved., Math., No. 10, 70–80 (1977).
M. M. Karchevskii, “An iterative scheme for a quasilinear elliptical equation on a polar grid,” in: Numerical Methods in the Mechanics of Continuous Medium [in Russian], No. 4, No. 2, VTs SO AN SSSR (1973), pp. 84–92.
M. I. Bakirova and I. V. Fryazinov, “On the iterative method of variable directions for the difference Poisson equation in curvilinear orthogonal coordinates,” Zh. Vychisl. Mat. Mat. Fiz.,13, No. 6 (1973).
M. M. Karchevskii and A. D. Lyashko, Difference Schemes for Nonlinear Problems in Mathematical Physics [in Russian], Kazan (1976).
A. A. Samarskii and E. S. Nikolaev, Methods of Solution of Finite-Difference Equations [in Russian], Nauka, Moscow (1978).
Additional information
Translated from Issledovaniya po Prikladnoi Matematike, No. 9, pp. 3–8, 1981.
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Karchevskii, M.M. An iterative variable direction scheme for the solution of the plane problem of elasticity theory on a polar grid. J Math Sci 46, 2159–2163 (1989). https://doi.org/10.1007/BF01097130
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DOI: https://doi.org/10.1007/BF01097130