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Calculation of eigenvalues of the Helmholtz equation by an integral equation
Author(s) -
de Mey G.
Publication year - 1976
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620100105
Subject(s) - helmholtz equation , eigenvalues and eigenvectors , mathematics , electric field integral equation , mathematical analysis , integral equation , helmholtz free energy , summation equation , boundary (topology) , matrix differential equation , integro differential equation , boundary value problem , partial differential equation , differential equation , riccati equation , physics , quantum mechanics
Abstract A method is presented to calculate the eigenvalues of the Helmholtz equation Δ 2 ø + k 2 ø = 0 in a two‐dimensional area when ø vanishes on the boundary. The method is based on an integral equation, which can be easily solved numerically. Results obtained for circular and rectangular geometries are also given and compared to the exact values.