Práger, Milan Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle. (English) Zbl 0940.35059 Appl. Math., Praha 43, No. 4, 311-320 (1998). 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. Reviewer: Jan Zítko (Praha) Cited in 1 ReviewCited in 19 Documents MSC: 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs 65Z05 Applications to the sciences Keywords:Laplace operator; boundary value problem; eigenvalues; eigenfunctions PDFBibTeX XMLCite \textit{M. Práger}, Appl. Math., Praha 43, No. 4, 311--320 (1998; Zbl 0940.35059) Full Text: DOI EuDML References: [1] Křížek, M., Neittaanmäki, P.: Finite Element Approximaton of Variational Problems and Applications. Longman Scientific & Technical, Harlow, 1990. · Zbl 0708.65106 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.