Laplace’s and Poisson’s Equations in a Semi-Disc under the Dirichlet-Neumann Mixed Boundary Condition

Authors

DOI:

https://doi.org/10.5540/tcam.2023.024.02.00191

Keywords:

Laplace, Poisson, semi-disk, Dirichlet, Neumann, Green's, images.

Abstract

In this work, the solution of Poisson's equation in a semi-disc under a Dirichlet boundary condition at the base and a Neumann boundary condition on the circumference is calculated. The solution is determined in terms of Green's function, which is calculated in two ways, by the method of images and by solving its equation. In the particular case of Laplace's equation, it is presented a second way to solve it, which uses separation of variables and a Fourier transform.

Author Biography

R. T. Couto, Universidade Federal Fluminense Instituto de Matemática e Estatística

Universidade Federal Fluminense

Instituto de Matemática e Estatística

Departamento de Matemática Aplicada

Professor Associado 4

References

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Published

2023-05-24

How to Cite

Couto, R. T. (2023). Laplace’s and Poisson’s Equations in a Semi-Disc under the Dirichlet-Neumann Mixed Boundary Condition. Trends in Computational and Applied Mathematics, 24(2), 191–210. https://doi.org/10.5540/tcam.2023.024.02.00191

Issue

Vol. 24 No. 2 (2023)

Section

Original Article

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