New solution and analytical techniques of the implicit numerical method for the anomalous subdiffusion equation

作者：Zhuang P^*; Liu F; Anh V; Turner I

来源：SIAM Journal on Numerical Analysis, 2008, 46(2): 1079-1095.

DOI：10.1137/060673114

• anomalous subdiffusion equation
• implicit numerical method
• stability
• convergence
• fractional integro-differential equation

A physical-mathematical approach to anomalous diffusion is based on a generalized diffusion equation containing derivatives of fractional order. In this paper, an anomalous subdiffusion equation (ASub-DE) is considered. A new implicit numerical method (INM) and two solution techniques for improving the order of convergence of the INM for solving the ASub-DE are proposed. The stability and convergence of the INM are investigated by the energy method. Some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and supporting theoretical results can also be applied to other fractional integro-differential equations and higher-dimensional problems.

• 出版日期2008
• 单位厦门大学; 华南理工大学