Solution of Helmholtz's equation in the plane with an elliptical hole

Sukhorolsky M.
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Abstract: 
General approach to constructing solutions of boundary value problems for Helmholtz's equations is considered. By transforming coordinates applying conforming mappings of corresponding domains onto the circle, a set of solutions of Helmholtz's equation in different coordinate systems is obtained. Solutions of boundary value problems for this equation in the plane with an elliptical hole are constructed.
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Bibliography: 
Math. Model. Comput. Vol.1, No.2, pp.256-263 (2014)