@article {
author = {afshari, elham},
title = {A New Implicit Finite Difference Method for Solving Time Fractional Diffusion Equation},
journal = {International Journal of Mathematical Modelling & Computations},
volume = {8},
number = {1 (WINTER)},
pages = {1-14},
year = {2018},
publisher = {Islamic Azad University, Central tehran Branch},
issn = {2228-6225},
eissn = {2228-6233},
doi = {},
abstract = {In this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in the Caputo sense. We propose a new finite difference method for solving time fractional diffu- sion equation. In our method firstly, we transform the Caputo derivative into Riemann-Liovill derivative. The stability and convergence of this method are investigated by a Fourier analysis. We show that this method is uncondition- ally stable and convergent with the convergence order O( 2+h2), where t and h are time and space steps respectively. Finally, a numerical example is given that confirms our theoretical analysis and the behavior of error is examined to verify the order of convergence.},
keywords = {fractional derivative,finite difference method,Stability and convergence,Fourier analysis,time fractional diffusion equation},
url = {http://ijm2c.iauctb.ac.ir/article_663807.html},
eprint = {http://ijm2c.iauctb.ac.ir/article_663807_53c9c99caec4e84548d94062b368e1f6.pdf}
}