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

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
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 ( 0000-0001-9066-7922)

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