IJPAM: Volume 49, No. 4 (2008)

APPROXIMATE APPROXIMATIONS AND
THE POISSON EQUATION IN THE WHOLE SPACE

Werner Varnhorn
Faculty of Mathematics
University of Kassel
Kassel, 34109, GERMANY
e-mail: varnhorn@mathematik.uni-kassel.de


Abstract.The method of approximate approximations is based on generating functions representing an approximate partition of the unity, only. In the present paper this method is used for the numerical solution of the Poisson equation in $\,\R^n\;(n = 2, 3)$. The corresponding approximate volume potentials will be computed explicitly in these cases, containing a one-dimensional integral, only. Numerical simulations show the efficiency of the method and confirm the expected convergence of essentially second order, depending on the smoothness of the data.

Received: August 14, 2008

AMS Subject Classification: 31B10, 35J05, 41A30, 65N12, 76D07

Key Words and Phrases: approximate approximations, volume potentials, Poisson equation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 49
Issue: 4