TY - JOUR
ID - 663807
TI - A New Implicit Finite Difference Method for Solving Time Fractional Diffusion Equation
JO - International Journal of Mathematical Modelling & Computations
JA - IJM2C
LA - en
SN - 2228-6225
AU - afshari, elham
AD - Islamic Azad University,khomain Branch
Y1 - 2018
PY - 2018
VL - 8
IS - 1 (WINTER)
SP - 1
EP - 14
KW - fractional derivative
KW - finite difference method
KW - Stability and convergence
KW - Fourier analysis
KW - time fractional diffusion equation
DO -
N2 - 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.
UR - http://ijm2c.iauctb.ac.ir/article_663807.html
L1 - http://ijm2c.iauctb.ac.ir/article_663807_53c9c99caec4e84548d94062b368e1f6.pdf
ER -