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A Compact ADI Scheme for Two-dimensional Caputo-Hadamard Fractional Sub-diffusion Equations
Guan Kai-jing, Mo Yan, Wang Zhi-bo
- School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510520, China
CLC Number:
- O241.8
| [1] KILBAS A, SRIVASTAVA H M, TRUJILLO J J. Theory and applications of fractional differential equations[J]. North-Holland Mathematics Studies, 2006, 204: 1-523. [2] HILFER R. Applications of fractional calculus in physics[M]. London: World Scientific, 2000. [3] UCHAIKIN V V. Fractional derivatives for physicists and engineers[M]. Heidelberg: Springer, 2013. [4] PUROHIT S D. Solutions of fractional partial differential equations of quantum mechanics [J]. Advances in Applied Mathematics and Mechanics, 2013, 5(5): 13. [5] LI C P, LI Z Q, WANG Z. Mathematical analysis and the local discontinuous Galerkin method for Caputo-Hadamard fractional partial differential equation [J]. Journal of Scientific Computing, 2020, 85(2): 41-68. [6] LI C P, LI Z Q. Stability and logarithmic decay of the solution to Hadamard-type fractional differential equation [J]. Journal of Nonlinear Science, 2021, 31(2): 31-91. [7] OU C X, CEN D K, VONG S W, et al. Mathematical analysis and numerical methods for Caputo-Hadamard fractional diffusion-wave equations [J]. Applied Numerical Mathematics, 2022, 177: 34-57. [8] WANG Z B, OU C X, VONG S W. A second-order scheme with nonuniform time grids for Caputo-Hadamard fractional sub-diffusion equations [J]. Journal of Computational and Applied Mathematics, 2022, 414: 114448. [9] LIAO H L, SUN Z Z. Maximum error estimates of ADI and compact ADI methods for solving parabolic equations [J]. Numerical Methods Partial Differential Equation, 2010, 26: 37-60. [10] WANG Z B, VONG S W. A high-order ADI scheme for the two-dimensional time fractional diffusion-wave equation [J]. International Journal Computer Mathematics, 2015, 92(5): 970-979. [11] 彭家, 黎丽梅, 肖华, 等. 二维粘弹性棒和板问题ADI有限差分法[J]. 湖南理工学院学报:自然科学版, 2022, 35(1): 4-9. PENG J, LI L M, XIAO H, et al. ADI finite difference method for two dimensional viscoelastic rod and plate problems [J]. Hunan Institute of Science and Technology:Natural Sciences, 2022, 35(1): 4-9. [12] WANG Z B, CEN D K, MO Y. Sharp error estimate of a compact L1-ADI scheme for the two-dimensional time-fractional integro-differential equation with singular kernels [J]. Applied Numerical Mathematics, 2021, 159: 190-203. [13] 朱晨怡, 王廷春. 二维复值Ginzburg-Landau方程的一个高阶紧致ADI差分格式[J]. 南京航空航天大学学报, 2019(3): 341-349. ZHU C Y, WANG T C. High-order compact alternating direction implicit scheme for complex Ginzburg-Landau equations in two dimensions [J]. Nanjing University of Aeronautics & Astronautics, 2019(3): 341-349. [14] FAN E Y, LI C P, LI Z Q. Numerical approaches to Caputo-Hadamard fractional derivatives with applications to long-term integration of fractional differential systems [J]. Communications in Nonlinear Science and Numerical Simulation, 2022, 106: 106096. [15] GAO G H, SUN Z Z. A compact finite difference scheme for the fractional sub-diffusion equations [J]. Journal of Computational Physics, 2011, 230(3): 586-595. |
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Tel：020-37626653,020-37626139,020-37626396
Email：xbzrb@gdut.edu.cn
Supported:Beijing Magtech