A New Implicit Finite Dierence Method for Solving Time Fractional Diusion Equation

In this paper, a time fractional diusion equation on a nite domain is considered. The time fractional diusion equation is obtained from the standard diusion equation by replacing the rst order time derivative by a fractional derivative of order 0 < 6 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 nite dierence method for solving time fractional diusion equation. In our method rstly, 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 unconditionally stable and convergent with the con- vergence order O(2 + h2), where and h are time and space steps respectively. Finally, a numerical example is given that conrms our theoretical analysis and the behavior of error is examined to verify the order of convergence.