Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle

Milan Práger

Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle

Milan Práger

Applications of Mathematics (1998)

Volume: 43, Issue: 4, page 311-320
ISSN: 0862-7940

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Abstract

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A boundary value problem for the Laplace equation with Dirichlet and Neumann boundary conditions on an equilateral triangle is transformed to a problem of the same type on a rectangle. This enables us to use, e.g., the cyclic reduction method for computing the numerical solution of the problem. By the same transformation, explicit formulae for all eigenvalues and all eigenfunctions of the corresponding operator are obtained.

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Práger, Milan. "Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle." Applications of Mathematics 43.4 (1998): 311-320. <http://eudml.org/doc/33013>.

@article{Práger1998,
abstract = {A boundary value problem for the Laplace equation with Dirichlet and Neumann boundary conditions on an equilateral triangle is transformed to a problem of the same type on a rectangle. This enables us to use, e.g., the cyclic reduction method for computing the numerical solution of the problem. By the same transformation, explicit formulae for all eigenvalues and all eigenfunctions of the corresponding operator are obtained.},
author = {Práger, Milan},
journal = {Applications of Mathematics},
keywords = {Laplace operator; boundary value problem; eigenvalues; eigenfunctions; Laplace operator; boundary value problem; eigenvalues; eigenfunctions},
language = {eng},
number = {4},
pages = {311-320},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle},
url = {http://eudml.org/doc/33013},
volume = {43},
year = {1998},
}

TY - JOUR
AU - Práger, Milan
TI - Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle
JO - Applications of Mathematics
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 43
IS - 4
SP - 311
EP - 320
AB - A boundary value problem for the Laplace equation with Dirichlet and Neumann boundary conditions on an equilateral triangle is transformed to a problem of the same type on a rectangle. This enables us to use, e.g., the cyclic reduction method for computing the numerical solution of the problem. By the same transformation, explicit formulae for all eigenvalues and all eigenfunctions of the corresponding operator are obtained.
LA - eng
KW - Laplace operator; boundary value problem; eigenvalues; eigenfunctions; Laplace operator; boundary value problem; eigenvalues; eigenfunctions
UR - http://eudml.org/doc/33013
ER -

References

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Finite Element Approximaton of Variational Problems and Applications, Longman Scientific & Technical, Harlow, 1990. (1990) MR1066462

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