%0 Journal Article
%T A New Implicit Finite Difference Method for Solving Time Fractional Diffusion Equation
%J International Journal of Mathematical Modelling & Computations
%I Islamic Azad University, Central tehran Branch
%Z 2228-6225
%A afshari, elham
%D 2018
%\ 01/01/2018
%V 8
%N 1 (WINTER)
%P 1-14
%! A New Implicit Finite Difference Method for Solving Time Fractional Diffusion Equation
%K fractional derivative
%K finite difference method
%K Stability and convergence
%K Fourier analysis
%K time fractional diffusion equation
%R
%X 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.
%U http://ijm2c.iauctb.ac.ir/article_663807_53c9c99caec4e84548d94062b368e1f6.pdf