Numerical solution of Poisson's equation using radial basis function networks on the polar coordinate

Authors:
A. Aminataei;M. M. Mazarei
Affiliations:
Department of Mathematics, Faculty of Science, K. N. Toosi University of Technology, P.O. Box: 16315-1618, Tehran, Iran;Department of Mathematics, Faculty of Science, K. N. Toosi University of Technology, P.O. Box: 16315-1618, Tehran, Iran
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

This paper introduces a variant of direct and indirect radial basis function networks (DRBFNs and IRBFNs) for the numerical solution of Poisson's equation. We use transformation from Cartesian coordinates to polar ones and use DRBFN and IRBFN methods on the basis of a multiquadric approximation scheme. We have experienced that the result shows better accuracy than previously known ones. Also, our new way of solution does not influence the condition number.