Laplace’s and Poisson’s Equations in a Semi-Disc under the Dirichlet-Neumann Mixed Boundary Condition
DOI:
https://doi.org/10.5540/tcam.2023.024.02.00191Keywords:
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.References
D. G. Zill and M. R. Cullen, Differential Equations with Boundary-Value Prob lems. Belmont, CA: Brooks/Cole, 7 ed., 2009.
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products. Amsterdan: Academic Press (Elsevier), 2007.
J. D. Jackson, Classical Electrodynamics. New York: John Wiley & Sons, 3 ed., 1999.
D. G. Duffy, Green’s Functions with Applications. Boca Raton: Chapman & Hall/CRC, 2001.
A. N. Tijonov and A. A. Samarsky, Ecuaciones de la Fisica Matematica. Moscow: Editorial Mir (translated from Russian to Spanish), 2 ed., 1980.
E. C. Zachmanoglou and D. W. Thoe, Introduction to Partial Differential Equa tions with Applications. New York: Dover Publications, 1986.
I. Rubinstein and L. Rubinstein, Partial Differential Equations. Cambridge University Press, 1998.
G. Barton, Elements of Green’s Functions and Propagation: Potentials, Diffu sion, and Waves. Oxford University Press, 1989.
E. Butkov, Mathematical Physics. Reading, MA: Addison-Wesley, 1973.
J. Franklin, Classical Electromagnetism. Mineola, NY: John Wiley & Sons, 2 ed., 2017.
G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists. San Diego: Academic Press, 5 ed., 2001.
R. Reynolds and A. Stauffer, “A method for evaluating definite integrals in terms of special functions with examples,” International Mathematical Forum, vol. 15, no. 5, pp. 235–244, 2020.
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