TY - JOUR
T1 - An Implicit Difference-ADI Method for the Two-dimensional Space-time Fractional Diffusion Equation
JF - IJMSI
JO - IJMSI
VL - 11
IS - 2
UR - http://ijmsi.ir/article-1-492-en.html
Y1 - 2016
SP - 71
EP - 86
KW Two-dimensional fractional differential equation
KW Space-time fractional diffusion equation
KW Implicit difference method
KW Alternating directions implicit methods
N2 - Fractional order diffusion equations are generalizations of classical diffusion equations which are used to model in physics, finance, engineering, etc. In this paper we present an implicit difference approximation by using the alternating directions implicit (ADI) approach to solve the two-dimensional space-time fractional diffusion equation (2DSTFDE) on a finite domain. Consistency, unconditional stability, and therefore first-order convergence of the method are proven. Some numerical examples with known exact solution are tested, and the behavior of the errors are analyzed to demonstrate the order of convergence of the method.
M3 10.7508/ijmsi.2016.02.005
ER -