Geodesic
Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle for the discrete case
Applications of Mathematics, Tome 46 (2001) no. 3, pp. 231-239.

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A discretized boundary value problem for the Laplace equation with the Dirichlet and Neumann boundary conditions on an equilateral triangle with a triangular mesh is transformed into a problem of the same type on a rectangle. Explicit formulae for all eigenvalues and all eigenfunctions are given.
DOI : 10.1023/A:1013744008028
Classification : 35J05, 35P10, 35R10, 65N06, 65N25
Keywords: discrete Laplace operator; discrete boundary value problem; eigenvalues; eigenfunctions 
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Práger, Milan. Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle for the discrete case. Applications of Mathematics, Tome 46 (2001) no. 3, pp. 231-239. doi : 10.1023/A:1013744008028. http://geodesic.mathdoc.fr/articles/10.1023/A:1013744008028/

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