Year: 2025
Author: Andreas Karageorghis, Daniel Lesnic
Annals of Applied Mathematics, Vol. 41 (2025), Iss. 2 : pp. 219–238
Abstract
In this paper, we develop the method of fundamental solutions (MFS) for solving boundary value problems in the field of optical fluorescence. The governing system of diffusion-absorption equations for the excitation and emission fluences is transformed into a single fourth-order partial differential equation whose fundamental solution can be expressed as the difference of two fundamental solutions of the complex Helmholtz equation. The numerically obtained results confirm the accuracy of the MFS when compared with an available analytical solution. Numerical results are also provided for a physical application in optical fluorescence. Furthermore, extensions to three dimensions along with numerical verification are performed.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2025-0010
Annals of Applied Mathematics, Vol. 41 (2025), Iss. 2 : pp. 219–238
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Optical fluorescence method of fundamental solutions elliptic equations.