A Weighted ADI Scheme for Subdiffusion Equations

详细信息    查看全文

• 作者：Hong-lin Liao ; Ying Zhao ; Xing-hu Teng
• 关键词：Subdiffusion equation ; ADI scheme ; Discrete energy method ; Stability and convergence ; Nonuniform time mesh
• 刊名：Journal of Scientific Computing
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：69
• 期：3
• 页码：1144-1164
• 全文大小：568 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algorithms
  Computational Mathematics and Numerical Analysis
  Applied Mathematics and Computational Methods of Engineering
  Mathematical and Computational Physics
  
• 出版者：Springer Netherlands
• ISSN：1573-7691
• 卷排序：69

文摘

A weighted ADI scheme is proposed for solving two-dimensional anomalous diffusion equations with the fractional Caputo derivative. The Alikhanov formula (J Comput Phys 280:424–438, 2015) with a weaker assumption is applied to approximate the fractional derivative and a high-order perturbed term of temporal order \(1+2\alpha \) is added to the pure implicit approach. By using the discrete energy method, it is proven that the ADI scheme is stable and convergent with the temporal order of \(\min \{1+2\alpha ,2\}\) such that it achieves second-order time accuracy when \(\frac{1}{2}\le \alpha <1\). Numerical experiments are included to support the theoretical analysis. Application of suggested method to the solution which lacks the smoothness near the initial time is examined by employing a class of nonuniform meshes refined near the singular point.