Approximate analytic solution of the Dirichlet problems for Laplace’s equation in planar domains by a perturbation method |
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| Authors: | E Di Costanzo A Marasco |
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| Affiliation: | a Department of Fundamental and Applied Sciences for Engineering, Sapienza University of Rome, Via A. Scarpa 16, 00161, Rome, Italyb Department of Mathematics and Applications “R. Caccioppoli”, University of Naples Federico II, Via Cintia, 80126, Naples, Italy |
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| Abstract: | In this paper, we propose a regular perturbation method to obtain approximate analytic solutions of exterior and interior Dirichlet problems for Laplace’s equation in planar domains. This method, starting from a geometrical perturbation of these planar domains, reduces our problems to a family of classical Dirichlet problems for Laplace’s equation in a circle. Numerical examples are given and comparisons are made with the solutions obtained by other approximation methods. |
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| Keywords: | Laplace&rsquo s equation Planar interior and exterior Dirichlet problems Regular perturbation method |
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