Properties of a method of fundamental solutions for the parabolic heat equation


We show that a set of fundamental solutions to the parabolic heat equation, with each element in the set corresponding to a point source located on a given surface with the number of source points being dense on this surface, constitute a linearly independent and dense set with respect to the standard inner product of square integrable functions, both on lateral- and time-boundaries. This result leads naturally to a method of numerically approximating solutions to the parabolic heat equation denoted a method of fundamental solutions (MFS). A discussion around convergence of such an approximation is included.

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Divisions: College of Engineering & Physical Sciences > School of Informatics and Digital Engineering > Mathematics
College of Engineering & Physical Sciences > Systems analytics research institute (SARI)
Additional Information: © 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Uncontrolled Keywords: fundamental solution,parabolic heat equation,Applied Mathematics
Publication ISSN: 1873-5452
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Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
PURE Output Type: Article
Published Date: 2017-03
Published Online Date: 2016-10-19
Accepted Date: 2016-08-30
Submitted Date: 2016-07-11
Authors: Johansson, B. Tomas (ORCID Profile 0000-0001-9066-7922)

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