Solutions of boundary value problems for the Helmholtz equation in simply connected domains of the complex plane (Q2831359)
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scientific article; zbMATH DE number 6647295
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Solutions of boundary value problems for the Helmholtz equation in simply connected domains of the complex plane |
scientific article; zbMATH DE number 6647295 |
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2 November 2016
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Helmholtz equation
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solution for circle
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solution for plane with cut
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Solutions of boundary value problems for the Helmholtz equation in simply connected domains of the complex plane (English)
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In the paper the conformal mappings of simply connected domains onto the circle are used to construct bases in the spaces of functions being analytical in these domains. The obtained basic functions are bi-orthogonal with the Faber polynomials. Based on the analytical functions expansions into series in basic functions systems, the solutions of boundary value problems for the Helmholtz equation are determined, whose boundary values coincide with the boundary values of these functions.
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