Table of Contents Author Guidelines Submit a Manuscript
Journal of Function Spaces
Volume 2017 (2017), Article ID 3679526, 8 pages
https://doi.org/10.1155/2017/3679526
Research Article

A Compact Difference Scheme for Solving Fractional Neutral Parabolic Differential Equation with Proportional Delay

1School of Statistics & Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China
2School of Finance, Zhongnan University of Economics and Law, Wuhan 430073, China

Correspondence should be addressed to Yanli Zhou; moc.liamg@7058uohzly and Xiangyu Ge; moc.361@eg_uygnaix

Received 5 July 2017; Accepted 17 September 2017; Published 18 October 2017

Academic Editor: Xinguang Zhang

Copyright © 2017 Wei Gu 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. A. V. Rezounenko and J. Wu, “A non-local PDE model for population dynamics with state-selective delay: local theory and global attractors,” Journal of Computational and Applied Mathematics, vol. 190, no. 1-2, pp. 99–113, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  2. B. Zubik-Kowal, “Solutions for the cell cycle in cell lines derived from human tumors,” Computational and Mathematical Methods in Medicine. An Interdisciplinary Journal of Mathematical, Theoretical and Clinical Aspects of Medicine, vol. 7, no. 4, pp. 215–228, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. D. Li, C. Zhang, and W. Wang, “Long time behavior of non-Fickian delay reaction-diffusion equations,” Nonlinear Analysis: Real World Applications, vol. 13, no. 3, pp. 1401–1415, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. Z.-X. Sun and Z. B. Zhang, “A linearized compact difference scheme for a class of nonlinear delay partial differential equations,” Applied Mathematical Modelling: Simulation and Computation for Engineering and Environmental Systems, vol. 37, no. 3, pp. 742–752, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  5. Q. Zhang and C. Zhang, “A compact difference scheme combined with extrapolation techniques for solving a class of neutral delay parabolic differential equations,” Applied Mathematics Letters, vol. 26, no. 2, pp. 306–312, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. W. Gu, “A compact difference scheme for a class of variable coefficient quasilinear parabolic equations with delay,” Abstract and Applied Analysis, Article ID 810352, Art. ID 810352, 8 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. D. Li, C. Zhang, and J. Wen, “A note on compact finite difference method for reaction-diffusion equations with delay,” Applied Mathematical Modelling: Simulation and Computation for Engineering and Environmental Systems, vol. 39, no. 5-6, pp. 1749–1754, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. C. R. Jin, Z. H. Yu, and R. N. Qu, “An implicit difference scheme for solving a neutral delay parabolic differential equation,” Journal of Shandong University. Natural Science. Shandong Daxue Xuebao. Lixue Ban, vol. 46, no. 8, pp. 13–16, 2011. View at Google Scholar · View at MathSciNet
  9. R. Metzler and J. Klafter, “The random walk's guide to anomalous diffusion: a fractional dynamics approach,” Physics Reports, vol. 339, pp. 1–77, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  10. S. Chen, F. Liu, I. Turner, and V. Anh, “An implicit numerical method for the two-dimensional fractional percolation equation,” Applied Mathematics and Computation, vol. 219, no. 9, pp. 4322–4331, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. F. A. Rihan, “Computational methods for delay parabolic and time-fractional partial differential equations,” Numerical Methods for Partial Differential Equations, vol. 26, no. 6, pp. 1556–1571, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. Q. Zhang, M. Ran, and D. Xu, “Analysis of the compact difference scheme for the semilinear fractional partial differential equation with time delay,” Applicable Analysis: An International Journal, vol. 96, no. 11, pp. 1867–1884, 2017. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. Z. Sun and X. Wu, “A fully discrete difference scheme for a diffusion-wave system,” Appl. Numer. Math, vol. 56, pp. 193–209, 2006. View at Google Scholar
  14. S. Chen, F. Liu, P. Zhuang, and V. Anh, “Finite difference approximations for the fractional Fokker-Planck equation,” Applied Mathematical Modelling: Simulation and Computation for Engineering and Environmental Systems, vol. 33, no. 1, pp. 256–273, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. Z. Z. Sun, The numerical methods for partial equations, Science Press, Beijing, China, 2005 (Chinese).