@Article{NMTMA-6-571,
author = {Hongmei Zhang and Shujun Shen},
title = {The Numerical Simulation of Space-Time Variable Fractional Order Diffusion Equation},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2013},
volume = {6},
number = {4},
pages = {571--585},
abstract = {<p style="text-align: justify;">Many physical processes appear to exhibit fractional order
behavior that may vary with time or space. The continuum of order in
the fractional calculus allows the order of the fractional operator
to be considered as a variable. Numerical methods and analysis of
stability and convergence of numerical scheme for the variable
fractional order partial differential equations are quite limited
and difficult to derive.
 This motivates us to develop efficient numerical methods as well as stability and convergence of the implicit numerical methods for the space-time
variable fractional order diffusion equation on a finite domain. It
is worth mentioning that here we use the Coimbra-definition variable time
fractional derivative
 which is more efficient from the numerical standpoint and is preferable for modeling dynamical systems.
 An implicit Euler approximation is proposed and then
the stability
 and convergence of the numerical scheme are investigated.
 &nbsp;Finally, numerical examples are provided to show that the implicit Euler approximation is computationally
 efficient.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2013.y12107},
url = {http://global-sci.org/intro/article_detail/nmtma/5919.html}
}