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ISRN Mathematical Physics
Volume 2012 (2012), Article ID 234516, 11 pages
doi:10.5402/2012/234516
Cubic Spline Iterative Method for Poissonโs Equation in Cylindrical Polar Coordinates
1Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi 110 007, India
2Department of Mathematics, Deenbandhu Chhotu Ram University of Science & Technology, Murthal 131039, India
Received 4 October 2011; Accepted 16 November 2011
Academic Editors: J.-C. Wallet and H. Zhou
Copyright © 2012 R. K. Mohanty et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Using nonpolynomial cubic spline approximation in - and finite difference in -direction, we discuss a numerical approximation of for the solutions of diffusion-convection equation, where and are grid sizes in - and -coordinates, respectively. We also extend our technique to polar coordinate system and obtain high-order numerical scheme for Poisson’s equation in cylindrical polar coordinates. Iterative method of the proposed method is discussed, and numerical examples are given in support of the theoretical results.