High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations (II)
Tóm tắt
Từ khóa
Tài liệu tham khảo
A. A. Alikhanov, A new difference scheme for the time fractional diffusion equation. J. Comput. Phys. 280 (2015), 424–438.
J. X. Cao, C. P. Li, Finite difference scheme for the time-space fractional diffusion equations. Centr. Eur. J. Phys. 11, No 10 (2013), 1440–1456.
C. Chen, F. Liu, I. Turner, V. Anh, A Fourier method for the fractional diffusion equation describing sub-diffusion. J. Comput. Phys. 227, No 2 (2007), 886–897.
J. X. Cao, C. P. Li, Y. Q. Chen, Compact differencemethod for solving the fractional reaction-subdiffusion equation with neumann boundary value condition. Int. J. Comput. Math. 92, No 1 (2015), 167–180.
G. Gao, Z. Sun, H. Zhang, A new fractional numerical differentiation formula to approximate the Caputo fractional derivative and its applications. J. Comput. Phys. 259 (2014), 33–50.
B. Jin, R. Lazarov, Z. Zhou, An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data. IMA J. Numer. Anal.; First Publ. online: Jan. 24, 2015; doi: 10.1093/imanum/dru063, 2015.
I. Karatay, N. Kale, S. R. Bayramoglu, A new difference scheme for time fractional heat equations based on the Crank-Nicholson method. Fract. Calc. Appl. Anal. 16, No 4 (2013), 892–910; DOI: 10.2478/s13540-013-0055-2; http://www.degruyter.com/view/j/fca.2013.16.issue-4/s13540-013-0055-2/s13540-013-0055-2.xml; http://link.springer.com/article/10.2478/s13540-013-0055-2.
C. P. Li, R. F. Wu, H. F. Ding, High-order approximation to Caputo derivative and Caputo-type advection-diffusion equation (I). Commun. Appl. Ind. Math. 7, No 1 (2015), In press.
C. P. Li, A. Chen, J. J. Ye, Numerical approaches to fractional calculus and fractional ordinary differential equation. J. Comput. Phys. 230, No 9 (2011), 3352–3368.
K. B. Oldham, J. Spanier, The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order. Academic Press, New York, 2006.
I. Podlubny, Fractional Differential Equations. Academic Press, San Diego, 1999.
I. Podlubny, A. Chechkin, T. Skovranek, Y. Chen, B. M. Vinagre Jara, Matrix approach to discrete fractional calculus II: Partial fractional differential equations. J. Comput. Phys. 228, No 8 (2009), 3137–3153.
E. Sousa, Numerical approximations for fractional diffusion equations via splines. Comput. Math. Appl. 62, No 3 (2011), 938–944.
E. Sousa, How to approximate the fractional derivative of order 1 < α ≤ 2. Int. J. Bifurcation Chaos. 22, No 4 (2012).
F. H. Zeng, C. P. Li, F. W. Liu, I. Turner, The use of finite difference/ element approaches for solving the time-fractional subdiffusion equation. SIAM J. Sci. Comput. 35, No 6 (2013), A2976–A3000.