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.
Original language | English |
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Pages (from-to) | 83-89 |
Number of pages | 7 |
Journal | Applied Mathematics Letters |
Volume | 65 |
Early online date | 19 Oct 2016 |
DOIs | |
Publication status | Published - Mar 2017 |
Bibliographical note
© 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/Keywords
- fundamental solution
- parabolic heat equation