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Advances in Numerical Analysis
Volume 2010 (2010), Article ID 352174, 17 pages
http://dx.doi.org/10.1155/2010/352174
Research Article

A Family of Sixth-Order Compact Finite-Difference Schemes for the Three-Dimensional Poisson Equation

Department of Mathematics, North Carolina A & T State University, Greensboro, NC 27411, USA

Received 24 October 2009; Accepted 17 March 2010

Academic Editor: Yin Nian He

Copyright © 2010 Yaw Kyei 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

We derive a family of sixth-order compact finite-difference schemes for the three-dimensional Poisson's equation. As opposed to other research regarding higher-order compact difference schemes, our approach includes consideration of the discretization of the source function on a compact finite-difference stencil. The schemes derived approximate the solution to Poisson's equation on a compact stencil, and thus the schemes can be easily implemented and resulting linear systems are solved in a high-performance computing environment. The resulting discretization is a one-parameter family of finite-difference schemes which may be further optimized for accuracy and stability. Computational experiments are implemented which illustrate the theoretically demonstrated truncation errors.