Solutions of Boundary-Value Problems in Discretized Volumes

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dc.contributor.authorMakai, Mihaly
dc.contributor.authorOrechwa, Yuri
dc.date.accessioned2020-07-07T19:14:20Z
dc.date.available2020-07-07T19:14:20Z
dc.date.issued2002-01-02
dc.description.abstractThe solution of a boundary-value problem in a volume discretized by finitely many copies of a tile is obtained via a Green's function. The algorithm for constructing the solution exploits results from graph and group theory. This technique produces integral equations on the internal and external boundaries of the volume and demonstrates that two permutation matrices characterize the symmetries of the volume. We determine the number of linearly independent solutions required over the tile and the conditions needed for two boundary-value problems to be isospectral. Our method applies group theoretical considerations to asymmetric volumes.
dc.description.departmentMathematics
dc.formatText
dc.format.extent20 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationMakai, M., & Orechwa, Y. (2002). Solutions of boundary-value problems in discretized volumes. <i>Electronic Journal of Differential Equations, 2002</i>(01), pp. 1-20.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/11979
dc.language.isoen
dc.publisherSouthwest Texas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.holderThis work is licensed under a Creative Commons Attribution 4.0 International License.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2002, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectBoundary value problem
dc.subjectCovering group
dc.subjectEquispectral volumes
dc.titleSolutions of Boundary-Value Problems in Discretized Volumes
dc.typeArticle

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