598
Views
26
CrossRef citations to date
0
Altmetric
Section B

A high-order ADI scheme for the two-dimensional time fractional diffusion-wave equation

&
Pages 970-979 | Received 23 Oct 2013, Accepted 12 Apr 2014, Published online: 21 May 2014

References

  • M. Cui, Compact finite difference method for the fractional diffusion equation, J. Comput. Phys. 228 (2009), pp. 7792–7804. doi: 10.1016/j.jcp.2009.07.021
  • M. Cui, Compact alternating direction implicit method for two-dimensional time fractional diffusion equation, J. Comput. Phys. 231 (2012), pp. 2621–2633. doi: 10.1016/j.jcp.2011.12.010
  • V. Ervin and J. Roop, Variational formulation for the stationary fractional advection dispersion equation, Numer. Methods. Partial. Differ. Equ. 22 (2006), pp. 558–576. doi: 10.1002/num.20112
  • G. Gao and Z. Sun, A compact finite difference scheme for the fractional sub-diffusion equations, J. Comput. Phys. 230 (2011), pp. 586–595. doi: 10.1016/j.jcp.2010.10.007
  • R. Gorenflo, Y. Luchko, and F. Mainardi, Wright functions as scale-invariant solutions of the diffusion-wave equation, J. Comput. Appl. Math. 118 (2000), pp. 175–191. doi: 10.1016/S0377-0427(00)00288-0
  • J. Huang, Y. Tang, L. Vázquez, and J. Yang, Two finite difference schemes for time fractional diffusion-wave equation, Numer. Algorithms 64 (2013), pp. 707–720. doi: 10.1007/s11075-012-9689-0
  • F. Mainardi, Fractional relaxation-oscillation and fractional diffusion-wave phenomena, Chaos Solitons Fractals 7 (1996), pp. 1461–1477. doi: 10.1016/0960-0779(95)00125-5
  • M. Meerschaert and C. Tadjeran, Finite difference approximations for fractional advection-dispersion flow equations, J. Comput. Appl. Math. 172 (2004), pp. 65–77. doi: 10.1016/j.cam.2004.01.033
  • A. Mohebbi, M. Abbaszade, and M. Dehghan, A high-order and unconditionally stable scheme for the modified anomalous fractional sub-diffusion equation with a nonlinear source term, J. Comput. Phys. 240 (2013), pp. 36–48. doi: 10.1016/j.jcp.2012.11.052
  • A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations, Springer, Berlin, 1997.
  • C. Tadjeran and M. Meerschaert, A second-order accurate numerical method for the two-dimensional fractional diffusion equation, J. Comput. Phys. 220 (2007), pp. 813–823. doi: 10.1016/j.jcp.2006.05.030
  • W. Tian, H. Zhou, and W. Deng, A class of second order difference approximations for solving space fractional diffusion equations, Math. Comput. Available at arXiv:1201.5949 [math.NA].
  • Z. Wang and S. Vong, Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation. Available at arXiv:1310.5298 [math.NA].
  • Y. Zhang, Z. Sun, and X. Zhao, Compact alternating direction implicit scheme for the two-dimensional fractional diffusion-wave equation, SIAM J. Numer. Anal. 50 (2012), pp. 1535–1555. doi: 10.1137/110840959

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.