Numerical Algorithms with High Spatial Accuracy for the Fourth-Order Fractional Sub-Diffusion Equations with the First Dirichlet Boundary Conditions

作者：Ji, Cui-cui; Sun, Zhi-zhong^*; Hao, Zhao-peng

来源：Journal of Scientific Computing, 2016, 66(3): 1148-1174.

DOI：10.1007/s10915-015-0059-7

• Fourth-order fractional sub-diffusion equation
• First Dirichlet boundary conditions
• Compact difference scheme
• Stability
• Convergence

In this paper, a compact algorithm for the fourth-order fractional sub-diffusion equations with first Dirichlet boundary conditions, which depict wave propagation in intense laser beams, is investigated. Combining the average operator for the spatial fourth-order derivative, the L1 formula is applied to approximate the temporal Caputo fractional derivative. A novel technique is introduced to deal with the first Dirichlet boundary conditions. Using mathematical induction method, we prove that the presented difference scheme is unconditionally stable and convergent by the energy method. The convergence order is in -norm. The outline for the two-dimensional problem is also considered. Finally, some numerical examples are provided to confirm the theoretical results.

• 出版日期2016-3
• 单位东南大学