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Journal of Applied Mathematics
Volume 2012, Article ID 575493, 13 pages
http://dx.doi.org/10.1155/2012/575493
Research Article

New Second-Order Finite Difference Scheme for the Problem of Contaminant in Groundwater Flow

1Jiangsu Provincial Key Laboratory for Numerical Simulation of Large-Scale Complex Systems, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, China
2School of Science, Lishui University, Lishui 323000, China

Received 5 April 2012; Revised 9 May 2012; Accepted 10 May 2012

Academic Editor: Khalida Inayat Noor

Copyright © 2012 Quanyong Zhu 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 develop a new efficient second-order finite difference scheme for two-dimensional problem of contaminant in groundwater flow. Theoretical analysis shows that the scheme is second-order convergence in the L2 norm and is unconditionally stable. Numerical results demonstrate that the error measures of the second-order scheme are several times smaller than those of the standard implicit finite difference scheme.