Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term

作者：Liu F^*; Yang C; Burrage K

来源：Journal of Computational and Applied Mathematics, 2009, 231(1): 160-176.

DOI：10.1016/j.cam.2009.02.013

• Implicit difference method
• Modified anomalous subdiffusion equation
• Nonlinear source terms
• Energy method
• Stability and convergence

In this paper, we consider a modified anomalous subdiffusion equation with a nonlinear source term for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. A new implicit difference method is constructed. The stability and convergence are discussed using a new energy method. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis.

• 出版日期2009-9-1
• 单位厦门大学