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

B. Tomas Johansson

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)83-89
Number of pages7
JournalApplied Mathematics Letters
Volume65
Early online date19 Oct 2016
DOIs
Publication statusPublished - 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

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