We consider the Dirichlet problem for the Laplace equation in a bounded cylindrical domain C:=D , where D is a starlike domain of the (x,y)-plane. We show how to construct the solution by using the Fourier series method. We derive some numerical results defining by means of the so called “superformula” introduced by J.Gielis. By using a computer algebra system we find a quite rapid convergence of the approximate solutions to the real one, with only possible exceptions corresponding to singular points in which oscillations recalling Gibbs’ phenomenon appear. Our findings are in agreement with the theoretical results on Fourier series due to L.Carleson.
Solution of the Dirichlet problem for the Laplace equation in general cylinder / Germano, Bruna; D., Caratelli; P. E., Ricci; M. X., He. - In: LECTURE NOTES OF TICMI. - ISSN 1512-0511. - STAMPA. - 10:(2009), pp. 20-34.
Solution of the Dirichlet problem for the Laplace equation in general cylinder.
GERMANO, Bruna;
2009
Abstract
We consider the Dirichlet problem for the Laplace equation in a bounded cylindrical domain C:=D , where D is a starlike domain of the (x,y)-plane. We show how to construct the solution by using the Fourier series method. We derive some numerical results defining by means of the so called “superformula” introduced by J.Gielis. By using a computer algebra system we find a quite rapid convergence of the approximate solutions to the real one, with only possible exceptions corresponding to singular points in which oscillations recalling Gibbs’ phenomenon appear. Our findings are in agreement with the theoretical results on Fourier series due to L.Carleson.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
