The Modified Helmholtz Equation on a Regular Hexagon - The Symmetric Dirichlet problem


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Article
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Authors
Fokas, Athanassios 
Kalimeris, Konstantinos 
Abstract

Using the unified transform, also known as the Fokas method, we analyse the modified Helmholtz equation in the regular hexagon with symmetric Dirichlet boundary conditions; namely, the boundary value problem where the trace of the solution is given by the same function on each side of the hexagon. We show that if this function is odd, then this problem can be solved in closed form; numerical verification is also provided.

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Journal ISSN
2075-1680
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Publisher
MDPI AG
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Sponsorship
Engineering and Physical Sciences Research Council (EP/N006593/1)