References
- P. Zhuang, F. Liu, V. Anh, and I. Turner, New Solution and Analytical Techniques of the Implicit Numerical Method for the Anomalous Subdiffusion Equation, SIAM J. Numer. Anal., vol. 46, pp. 1079–1095, 2008.
- M. Raberto, E. Scalas, and F. Mainardi, Waiting-Times and Returns in High-Frequency Financial Data: An Empirical Study, Physica A, vol. 314, pp. 749–755, 2002.
- L. Sabatelli, S. Keating, J. Dudley, and P. Richmond, Waiting Time Distributions in Financial Markets, Eur. Phys. J. B, vol. 27, pp. 273–275, 2002.
- R. Gorenflo and F. Mainardi, Fractional Calulus: Integral and Differential Equations of Fractional Order, in A. Carpinteri and F. Mainardi (eds.), Fractals and Fractional Calculus in Continuum Mechanics, pp. 223–276, Springer-Verlag, Wien and New York, 1997.
- F. Mainardi, Fractional Relaxation-Oscillation and Fractional Diffusion-Wave Phenomena, Chaos Soliton. Fract., vol. 7, pp. 1461–1477, 1996.
- I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
- D. Benson, S. Wheatcraft, and M. Meerschaert, Application of a Fractional Advection-Dispersion Equation, Water Resources Res., vol. 36, pp. 1403–1412, 2000.
- P. Zhuang and F. Liu, Implicit Difference Approximation for the Time Fractional Diffusion Equation, J. Appl. Math. Comput., vol. 22, pp. 87–99, 2006.
- R. Scherer, S. Kalla, L. Boyadjiev, and B. Al-Saqabi, Numerical Treatment of Fractional Heat Equations, Appl. Numer. Math., vol. 58, pp. 1212–1223, 2008.
- W. Deng and C. Li, The Evolution of Chaotic Dynamics for Fractional Unified System, Phys. Lett. A, vol. 372, pp. 401–407, 2008.
- I. Podlubny, A. Chechkin, T. Skovranek, Y. Chen, and B. M. Vinagre Jara, Matrix Approach to Discrete Fractional Calculus II: Partial Fractional Differential Equations, J. Comput. Phys., vol. 228, pp. 3137–3153, 2009.
- O. Marom and E. Momoniat, A Comparison of Numerical Solutions of Fractional Diffusion Models in Finance, Nonlinear Anal. Real World Appl., vol. 10, pp. 3435–3442, 2009.
- K. Wang and H. Wang, A Fast Characteristic Finite Difference Method for Fractional Advection-Diffusion Equations, Adv. Water Resources, vol. 34, pp. 810–816, 2011.
- S. Yuste and J. Murillo, A Finite Difference Method with Non-Uniform Timesteps for Fractional Diffusion Equations, Comput. Phys. Commun., vol. 183, pp. 2594–2600, 2012.
- M. Cui, Compact Alternating Direction Implicit Method for Two Dimensional Time Fractional Diffusion Equation, J. Comput. Phys., vol. 231, pp. 2621–2633, 2012.
- J. Ren, Z. Sun, and X. Zhao, Compact Difference Scheme for the Fractional Sub-Diffusion Equation with Neumann Boundary Conditions, J. Comput. Phys., vol. 232, pp. 456–467, 2013.
- Y. Zhang, Z. Sun, and H. Liao, Finite Difference Methods for the Time Fractional Diffusion Equation on Non-Uniform Meshes, J. Comput. Phys., vol. 265, pp. 195–210, 2014.
- S. Zhai, X. Feng, and Y. He, An Unconditionally Stable Compact ADI Method for Three-Dimensional Time-Fractional Convection-Diffusion Equation, J. Comput. Phys., vol. 269, pp. 138–155, 2014.
- S. Zhai, Z. Weng, D. Gui, and X. Feng, High-Order Compact Operator Splitting Method for Three-Dimensional Fractional Equation with Subdiffusion, Int. J. Heat Mass Transfer, vol. 84, pp. 440–447, 2015.
- S. Zhai, L. Qian, D. Gui, and X. Feng, A Block-Centered Characteristic Finite Difference Method for Convection-Dominated Diffusion Equation, Int. Commun. Heat Mass Transfer, vol. 61, pp. 1–7, 2015.
- Z. Lu, Y. Liao, D. Qian, J. McLaughlin, J. Derksen, and K. Kontomaris, Large Eddy Simulations of a Stirred Tank Using The Lattice Boltzmann Method on a Nonuniform Grid, J. Comput. Phys., vol. 181, pp. 675–704, 2002.
- T. Manteuffel and A. White, The Numerical Solution of Second-Order Boundary Value Problems on Nonuniform Meshes, Math. Comput., vol. 47, pp. 511–535, 1986.
- A. Weiser and M. Wheeler, On Convergence of Block-Centered Finite Differences for Elliptic Problems, SIAM J. Numer. Anal., vol. 25, pp. 351–375, 1988.
- H. Rui and H. Pan, A Block-Centered Finite Difference Method for the Darcy-Forchheimer Model, SIAM J. Numer. Anal., vol. 50, pp. 2612–2631, 2012.
- G. Huang, Q. Huang, and H. Zhan, Evidence of One-Dimensional Scale-Dependent Fractional Advection-Dispersion, J. Contam. Hydrol., vol. 85, pp. 53–71, 2006.
- M. Berger and J. Oliger, Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations, J. Comput. Phys., vol. 53, pp. 484–512, 1984.
- C. Min and F. Gibou, A Second Order Accurate Projection Method for the Incompressible Navier-Stokes Equations on Non-Graded Adaptive Grids, J. Comput. Phys., vol. 219, pp. 912–929, 2006.