Highly accurate approximations of Green's and Neumann functions on rectangular domains

Green's and Neumann functions of -Δ, where Δ is the Laplacian operator, on a rectangular domain are approximated to any desired degree of accuracy by finite series. Many applications require only a modest number of terms. Upper bounds for the errors in these approximations are also derived. The...

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Bibliographic Details
Published in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2001-04, Vol.457 (2008), p.767-772
Main Authors: McCann, R.C., Hazlett, R.D., Babu, D.K.
Format: Article
Language:English
Subjects:
Accuracy
Analysis
Approximation
Green's Functions
Greens function
Infinite series
Laplace
Mathematical functions
Neumann
Research Article
Series convergence
Trigonometric identities
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Summary:Green's and Neumann functions of -Δ, where Δ is the Laplacian operator, on a rectangular domain are approximated to any desired degree of accuracy by finite series. Many applications require only a modest number of terms. Upper bounds for the errors in these approximations are also derived. The approximating functions reveal the structural similarities and differences in Green's and Neumann functions.
ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.2000.0690