Johansson, B. Tomas
(2017).
Properties of a method of fundamental solutions for the parabolic heat equation.
Applied Mathematics Letters, 65
,
pp. 83-89.
Abstract
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.
Publication DOI: | https://doi.org/10.1016/j.aml.2016.08.021 |
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Divisions: | Engineering & Applied Sciences > Mathematics Engineering & Applied Sciences > Systems analytics research institute (SARI) |
Additional Information: | © 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ |
Uncontrolled Keywords: | fundamental solution,parabolic heat equation,Applied Mathematics |
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Related URLs: |
http://www.scop ... tnerID=8YFLogxK
(Scopus URL) |
Published Date: | 2017-03 |
Authors: |
Johansson, B. Tomas
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