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Matematicheskoe modelirovanie, 1996, Volume 8, Number 3, Pages 111–127
(Mi mm1553)
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Computational methods and algorithms
Parallel methods of solving singularly perturbed boundary value problems for elliptic equations
G. I. Shishkin, I. V. Tselischeva Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Abstract:
A Dirichlet problem is considered on a rectangle for singularly perturbed linear and quasilinear elliptic equations. When the perturbation parameter equals zero, elliptic equations degenerate into zero-order ones. Special iterative and iteration-free finite difference schemes (in particularly, the schemes using parallel computations) are constructed which converge uniformly with respect to the parameter. Schwarz' method is used to construct the schemes. Necessary and sufficient conditions are given for the solutions of the iterative difference schemes to converge uniformly with respect to the perturbing parameter as the number of iterations increases. It is shown that the use of schemes with parallel computations on multiprocessor computers provides the acceleration of computations.
Received: 26.04.1994
Citation:
G. I. Shishkin, I. V. Tselischeva, “Parallel methods of solving singularly perturbed boundary value problems for elliptic equations”, Matem. Mod., 8:3 (1996), 111–127
Linking options:
https://www.mathnet.ru/eng/mm1553 https://www.mathnet.ru/eng/mm/v8/i3/p111
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Abstract page: | 367 | Full-text PDF : | 128 | First page: | 1 |
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