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: | 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 http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| Uncontrolled Keywords: | fundamental solution,parabolic heat equation,Applied Mathematics |
| Publication ISSN: | 1873-5452 |
| Last Modified: | 19 Jun 2025 07:09 |
| Date Deposited: | 26 Oct 2016 14:55 |
| Full Text Link: | |
| 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
(
0000-0001-9066-7922)
|
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Version: Accepted Version
License: Creative Commons Attribution Non-commercial No Derivatives
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