Journal of Applied Mathematics

Method of Infinite System of Equations for Problems in Unbounded Domains

Dang Quang A and Tran Dinh Hung

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Many problems of mechanics and physics are posed in unbounded (or infinite) domains. For solving these problems one typically limits them to bounded domains and find ways to set appropriate conditions on artificial boundaries or use quasi-uniform grid that maps unbounded domains to bounded ones. Differently from the above methods we approach to problems in unbounded domains by infinite system of equations. In this paper we present starting results in this approach for some one-dimensional problems. The problems are reduced to infinite system of linear equations. A method for obtaining approximate solution with a given accuracy is proposed. Numerical experiments for several examples show the effectiveness of the offered method.

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J. Appl. Math., Volume 2012 (2012), Article ID 584704, 17 pages.

First available in Project Euclid: 2 January 2013

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Quang A, Dang; Dinh Hung, Tran. Method of Infinite System of Equations for Problems in Unbounded Domains. J. Appl. Math. 2012 (2012), Article ID 584704, 17 pages. doi:10.1155/2012/584704.

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