Karageorghis, A. The method of fundamental solutions for the calculation of the eigenvalues of the Helmholtz equation. (English) Zbl 0984.65111 Appl. Math. Lett. 14, No. 7, 837-842 (2001). Summary: We investigate the application of the method of fundamental solutions for the calculation of the eigenvalues of the Helmholtz equation in the plane subject to homogeneous Dirichlet boundary conditions. We present results for circular and rectangular geometries. Cited in 43 Documents MSC: 65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 35P15 Estimates of eigenvalues in context of PDEs Keywords:numerical examples; method of fundamental solutions; eigenvalues; Helmholtz equation PDF BibTeX XML Cite \textit{A. Karageorghis}, Appl. Math. Lett. 14, No. 7, 837--842 (2001; Zbl 0984.65111) Full Text: DOI References: [1] Kupradze, V.D., Potential methods in the theory of elasticity, (1965), Israel Program for Scientific Translations Jerusalem · Zbl 0188.56901 [2] Mathon, R.; Johnston, R.L., The approximate solution of elliptic boundary-value problems by fundamental solutions, SIAM J. numer. anal., 14, 638-650, (1977) · Zbl 0368.65058 [3] Fairweather, G.; Karageorghis, A., The method of fundamental solutions for elliptic boundary value problems, Adv. comput. math., 9, 69-95, (1998) · Zbl 0922.65074 [4] Golberg, M.A.; Chen, C.S., Discrete projection methods for integral equations, (1996), Computational Mechanics Southampton [5] De Mey, G., Calculation of eigenvalues of the Helmholtz equation by an integral equation, Int. J. numer. methods engng., 10, 59-66, (1976) · Zbl 0325.65049 [6] Courant, R.; Hilbert, D., Methods of mathematical physics, I, (1953), John Wiley New York, Chapter V · Zbl 0729.00007 [7] Fetter, A.L.; Waleckaa, J.D., Theoretical mechanics of particles and continua, (1980), McGraw-Hill New York, Chapter 8 [8] Abramowitz, M.; Stegun, I.A., Pocketbook of mathematical functions, (1984), Verlag Harri Deutsch Frankfurt am Main · Zbl 0643.33002 [9] Numerical algorithms group library mark 16, (1993), NAG(UK) Ltd, Wilkinson House Jordan Hill Road, Oxford, UK [10] Kitagawa, T., On the numerical stability of the method of fundamental solution applied to the Dirichlet problem, Japan J. appl. math., 5, 123-133, (1988) · Zbl 0644.65060 [11] Kitagawa, T., Asymptotic stability of the fundamental solution method, J. comput. appl. math., 38, 263-269, (1991) · Zbl 0752.65077 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.