New Solution and Analytical Techniques of the Implicit Numerical Method for the Anomalous Subdiffusion Equation

@article{Zhuang2008NewSA,
  title={New Solution and Analytical Techniques of the Implicit Numerical Method for the Anomalous Subdiffusion Equation},
  author={P. Zhuang and Fawang Liu and Vo V. Anh and Ian W. Turner},
  journal={SIAM J. Numerical Analysis},
  year={2008},
  volume={46},
  pages={1079-1095}
}
A physical-mathematical approach to anomalous diffusion is based on a generalized diffusion equation containing derivatives of fractional order. In this paper, an anomalous sub-diffusion 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… CONTINUE READING