A box-type scheme for fractional sub-diffusion equation with Neumann boundary conditions

作者：Zhao Xuan; Sun Zhi zhong^*

来源：Journal of Computational Physics, 2011, 230(15): 6061-6074.

DOI：10.1016/j.jcp.2011.04.013

• Neumann boundary conditions
• Sub-diffusion equation
• Box-type scheme
• Stability
• Convergence
• Energy method

Combining order reduction approach and L1 discretization, a box-type scheme is presented for solving a class of fractional sub-diffusion equation with Neumann boundary conditions. A new inner product and corresponding norm with a Sobolev embedding inequality are introduced. A novel technique is applied in the proof of both stability and convergence. The global convergence order in maximum norm is O(tau(2-alpha) + h(2)). The accuracy and efficiency of the scheme are checked by two numerical tests.

• 出版日期2011-7-1
• 单位东南大学