Table of Contents Author Guidelines Submit a Manuscript
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.

Linked References

  1. P. J. Dillon, “An analytical model of contaminant transport from diffuse sources in saturated porous media,” Water Resources Research, vol. 25, no. 6, pp. 1208–1218, 1989. View at Google Scholar
  2. N.-Z. Sun, “Applications of numerical methods to simulate the movement of contaminants in groundwater,” Environmental Health Perspectives, vol. 83, pp. 97–115, 1989. View at Google Scholar
  3. H. L. Li and J. J. Jiao, “Analytical solutions of tidal groundwater flow in coastal two-aquifer system,” Advances in Water Resources, vol. 25, no. 4, pp. 417–426, 2002. View at Publisher · View at Google Scholar
  4. G. Pelovska, “An improved explicit scheme for age-dependent population models with spatial diffusion,” International Journal of Numerical Analysis and Modeling, vol. 5, no. 3, pp. 466–490, 2008. View at Google Scholar
  5. P. Wang and Z. Zhang, “Quadratic finite volume element method for the air pollution model,” International Journal of Computer Mathematics, vol. 87, no. 13, pp. 2925–2944, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. Z. Zhang, “Error estimates for finite volume element method for the pollution in groundwater flow,” Numerical Methods for Partial Differential Equations, vol. 25, no. 2, pp. 259–274, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. J. Borggaard, T. Iliescu, and J. P. Roop, “Two-level discretization of the Navier-Stokes equations with r-Laplacian subgridscale viscosity,” Numerical Methods for Partial Differential Equations, vol. 28, no. 3, pp. 1056–1078, 2012. View at Publisher · View at Google Scholar
  8. J. J. Miñambres and M. de la Sen, “Application of numerical methods to the acceleration of the convergence of the adaptive control algorithms. The one-dimensional case,” Computers and Mathematics with Applications Part A, vol. 12, no. 10, pp. 1049–1056, 1986. View at Google Scholar
  9. D. Deng and Z. Zhang, “A new high-order algorithm for a class of nonlinear evolution equation,” Journal of Physics A, vol. 41, pp. 1–17, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. W. Z. Dai and R. Nassar, “An unconditionally stable finite difference scheme for solving a 3D heat transport equation in a sub-microscale thin film,” Journal of Computational and Applied Mathematics, vol. 145, no. 1, pp. 247–260, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. W. Q. Wang, “The alternating segment Crank-Nicolson method for solving convection-diffusion equation with variable coefficient,” Applied Mathematics and Mechanics, vol. 24, no. 1, pp. 29–38, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. M. Ganesh and K. Mustapha, “A Crank-Nicolson and ADI Galerkin method with quadrature for hyperbolic problems,” Numerical Methods for Partial Differential Equations. An International Journal, vol. 21, no. 1, pp. 57–79, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. Z. Zhang, “An economical difference scheme for heat transport equation at the microscale,” Numerical Methods for Partial Differential Equations, vol. 20, no. 6, pp. 855–863, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. Z. Z. Sun, Numerical Methods for Partial Differential Equations, Science Press, 2005.
  15. J. F. Lu and Z. Guan, Numerical Methods for Partial Differential Equations, Qinghua University Press, 2003.
  16. W. Hundsdorfer and J. G. Verwer, Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, vol. 33 of Springer Series in Computational Mathematics, Springer, Berlin, Germany, 2003.
  17. D. Liang and W. D. Zhao, “An optimal weighted upwinding covolume method on non-standard grids for convection-diffusion problems in 2D,” International Journal for Numerical Methods in Engineering, vol. 67, no. 4, pp. 553–577, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH