Fourier-like solution of the Dirichlet problem for the Laplace Equation in k-type Gielis domainsFourier-like solution of the Dirichlet problem for the Laplace Equation in k-type Gielis domains
Faculty of Sciences. Bioscience Engineering
Environmental Ecology & Microbiology (ENdEMIC)
Journal of pure and applied mathematics : advances and applications
5(2011):2, p. 99-111
University of Antwerp
The interior and exterior Dirichlet problems for the Laplace equation in k-type Gielis domains are analytically addressed by using a suitable Fourier-like technique. A dedicated numerical procedure based on the computer-aided algebra tool Mathematica© is developed in order to validate the proposed approach. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained. Computed results are found to be in good agreement with theoretical findings on Fourier series expansion presented by Carleson.