Economical Iterative Algorithms for Solving Stationary Problems of Mathematical Physics |
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Authors: | Abrashin V. N. Egorov A. A. Zhadaeva N. G. |
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Affiliation: | (1) Institute of Mathematics, Academy of Sciences of Belarus, Surganova 11, Minsk, Belarus;(2) State University of Belarus, Minsk, Belarus |
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Abstract: | We construct and investigate additive iterative methods of complete approximation for solving stationary problems of mathematical physics. We prove the convergence of the proposed methods and obtain error estimates without the requirement of commutativity of the decomposition operators. We provide the results of a computational experiment for a three-dimensional boundary-value problem. We consider possible generalizations of algorithms for equations with mixed derivatives and Navier–Stokes equation systems. |
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Keywords: | elliptic equation Navier– Stokes equation difference method iterative methods alternating-direction methods |
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