About this Journal Submit a Manuscript Table of Contents
ISRN Mathematical Physics
Volume 2012 (2012), Article ID 234516, 11 pages
http://dx.doi.org/10.5402/2012/234516
Research Article

Cubic Spline Iterative Method for Poisson’s 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 𝑥 - and finite difference in 𝑦 -direction, we discuss a numerical approximation of 𝑂 ( 𝑘 2 + 4 ) for the solutions of diffusion-convection equation, where 𝑘 > 0 and > 0 are grid sizes in 𝑦 - and 𝑥 -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.