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

B. Tomas Johansson

doi:10.1016/j.aml.2016.08.021

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

B. Tomas Johansson

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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
Pages (from-to)	83-89
Number of pages	7
Journal	Applied Mathematics Letters
Volume	65
Early online date	19 Oct 2016
DOIs	https://doi.org/10.1016/j.aml.2016.08.021
Publication status	Published - Mar 2017

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Keywords

fundamental solution
parabolic heat equation

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10.1016/j.aml.2016.08.021

Fundamental solutions for the parabolic heat equation
© 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Accepted author manuscript, 208 KBLicence: CC BY-NC-ND 3.0

Cite this

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AB - 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.

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VL - 65

SP - 83

EP - 89

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

ER -

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

Abstract

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