王志强1, 文立平1, 朱珍民2
王志强, 文立平, 朱珍民. 时间延迟扩散-波动分数阶微分方程有限差分方法[J]. 计算数学, 2019, 41(1): 82-90.
Wang Zhiqiang, Wen Liping, Zhu Zhenmin. FINITE DIFFERENCE METHOD FOR TIME DELAY DIFFUSION-WAVE FRACTIONAL DIFFERENTIAL EQUATIONS[J]. Mathematica Numerica Sinica, 2019, 41(1): 82-90.
Wang Zhiqiang1, Wen Liping1, Zhu Zhenmin2
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[1] Deng W. Finite element method for the space and time fractional Fokker-Planck eqations[J]. SIAM Journal on Numerical Analysis, 2008, 47(1):204-226.[2] 胡劲松, 胡朝浪, 郑茂渡.广义对称正则长波方程的一个拟紧致守恒差分算法[J].四川大学学报:自然科学版, 2010, 47(2):221.[3] Yao Shujun, Zhang Yongliang. Numerical solution of generalized Maxwell fluid fractional differential equation[J]. Computer Engineering and Applications, 2013, 49(12):41.[4] 杨晨航, 刘发旺.分数阶Relaxation-Oscillation方程的一种分数阶预估-校正方法[J].厦门大学学报:自然科学版, 2005, 44(6):761-765.[5] 章红梅, 刘发旺.时间分数阶电报方程的一种解技巧[J].厦门大学学报:自然科学版, 2007, 46(1):10-13.[6] Gelhar, Lynn and Welty, Claire and R. Rehfeldt, K. A critical review of data on field-scale dispersion in aquifers[J]. 1993, 29(01):1867-1869.[7] Xu M, Tan M. Theory analysis of genernal second order anomalous diffusion velocity field, stress field and eddy field in liquid[J]. Science in China:Series S, 2001, 31:626-637.[8] del-Castillo-Negrete, Diego and Carreras, Benjamin and Lynch, V. Fractional diffusion in plasma turbulence[J]. 2004, 11(07):3854-3864.[9] Meerschaert, Mark and Tadjeran, Charles. Finite difference approximations for two-sided spacefractional partial differential equations[J]. 2004, 56(03):80-90.[10] Tadjeran, Charles and Meerschaert, Mark and Scheffler, Hans-Peter. A second-order accurate numerical approximation for the fraction diffusion equation[J]. 2006, 213(03):205-213.[11] Shen Shujun, Liu F, Anh Vo. Numerical approximations and solution techniques for the space-time riesz-caputo fractional advection-diffusion equation[J]. Applied Mathematical Modelling, 2011, 56(03):383-403.[12] Bu W P, Liu X T, Tang Y F, Yang J Y. Finite element multigrid method for multi-term time fractional advection diffusion equations[J]. Int. J. Model. Simul. Sci. Comput., 2015, 6.[13] Yang J Y, Huang J F, Liang D M, Tang Y F. Numerical solution of fractional diffusion-wave equation based on fractional multistep method[J]. Applied Mathematical Modelling, 2014, 38(14):3652-3661.[14] Li Changpin, Ding Hengfei. Higher order finite difference method for the reaction and anomalousdiffusion equation[J]. Applied Mathematical Modelling, 2014, 38(15):3802-3821.[15] Dimitrov, Numerical approximatios for fractional differential equations[J]. Journal of Fractional Calculus and Applications, 2013, 5(22):1-45.[16] Vladimir V. Uchaikin. Fractional Derivatives for Physicists and Engineers[M], volume 1. Higher Education Press, 2013.[17] Liu Mingding. A numerical method for solving one fractional delay diffusion differential equation[J]. Henan Science, 2016, 34(2). |
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