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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 493406, 15 pages
http://dx.doi.org/10.1155/2013/493406
Research Article

Numerical Algorithms for the Fractional Diffusion-Wave Equation with Reaction Term

Department of Mathematics, Shanghai University, Shanghai 200444, China

Received 24 April 2013; Revised 24 June 2013; Accepted 24 June 2013

Academic Editor: Juan J. Trujillo

Copyright © 2013 Hengfei Ding and Changpin Li. 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.

Citations to this Article [13 citations]

The following is the list of published articles that have cited the current article.

  • Fanhai Zeng, Changpin Li, Fawang Liu, and Ian Turner, “The Use Of Finite Difference/Element Approaches For Solving The Time-Fractional Subdiffusion Equation,” Siam Journal on Scientific Computing, vol. 35, no. 6, pp. A2976–A3000, 2013. View at Publisher · View at Google Scholar
  • Changpin Li, and Hengfei Ding, “Higher order finite difference method for the reaction and anomalous-diffusion equation,” Applied Mathematical Modelling, vol. 38, no. 15-16, pp. 3802–3821, 2014. View at Publisher · View at Google Scholar
  • Zhi Mao, Aiguo Xiao, Zuguo Yu, and Long Shi, “Sinc-Chebyshev Collocation Method for a Class of Fractional Diffusion-Wave Equations,” The Scientific World Journal, vol. 2014, pp. 1–7, 2014. View at Publisher · View at Google Scholar
  • Rifang Wu, Hengfei Ding, and Changpin Li, “Determination of Coefficients of High-Order Schemes for Riemann-Liouville Derivative,” The Scientific World Journal, vol. 2014, pp. 1–21, 2014. View at Publisher · View at Google Scholar
  • Somayeh Mashayekhi, and Mohsen Razzaghi, “Numerical solution of the fractional Bagley-Torvik equation by using hybrid functions approximation,” Mathematical Methods in the Applied Sciences, vol. 39, no. 3, pp. 353–365, 2015. View at Publisher · View at Google Scholar
  • Faoziya Al-Shibani, and Ahmad Ismail, “Compact Crank-Nicolson and Du Fort-Frankel Method for the Solution of the Time Fractional Diffusion Equation,” International Journal Of Computational Methods, vol. 12, no. 6, 2015. View at Publisher · View at Google Scholar
  • Fanhai Zeng, “Second-Order Stable Finite Difference Schemes for the Time-Fractional Diffusion-Wave Equation,” Journal Of Scientific Computing, vol. 65, no. 1, pp. 411–430, 2015. View at Publisher · View at Google Scholar
  • Mehdi Dehghan, Mostafa Abbaszadeh, and Akbar Mohebbi, “Analysis of two methods based on Galerkin weak form for fractional diffusion-wave: Meshless interpolating element free Galerkin (IEFG) and finite elem,” Engineering Analysis With Boundary Elements, vol. 64, pp. 205–221, 2016. View at Publisher · View at Google Scholar
  • Mehdi Dehghan, and Mostafa Abbaszadeh, “A finite element method for the numerical solution of Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivatives,” Engineering with Computers, 2016. View at Publisher · View at Google Scholar
  • Jin-Feng Wang, Yang Liu, Min Zhang, and Hong Li, “Finite difference/H1-galerkin MFE procedure for a fractional water wave model,” Journal of Applied Analysis and Computation, vol. 6, no. 2, pp. 409–428, 2016. View at Publisher · View at Google Scholar
  • Mohammad Shahbazi Asl, and Mohammad Javidi, “An improved PC scheme for nonlinear fractional differential equations: Error and stability analysis,” Journal of Computational and Applied Mathematics, 2017. View at Publisher · View at Google Scholar
  • Yanping Chen, Yunqing Huang, Yin Yang, and Huayi Wei, “Spectral collocation method for the time-fractional diffusion-wave equation and convergence analysis,” Computers and Mathematics with Applications, vol. 73, no. 6, pp. 1218–1232, 2017. View at Publisher · View at Google Scholar
  • Wei Cai, Wen Chen, Fangying Song, Fanhai Zeng, and George Em Karniadakis, “Efficient two-dimensional simulations of the fractional Szabo equation with different time-stepping schemes,” Computers and Mathematics with Applications, vol. 73, no. 6, pp. 1286–1297, 2017. View at Publisher · View at Google Scholar