Error analysis of an explicit finite difference approximation for the space fractional diffusion equation with insulated ends

Abstract

The space fractional diffusion equation (?) is obtained from the classical diffusion equation by replacing the second space derivative by a fractional derivative of order ?, 1 ? ? ? 2 . Numerical methods associated with integer-order differential equation, have been extensively treated. On the other hand, studies of the numerical methods and error estimates of fractional order differential equations are quite limited to date. Here, we propose an explicit finite difference approximation (?) for ?. An error analysis of the explicit numerical method for ? with insulated ends is discussed. We derive the scaling restriction of the stability and convergence of the explicit numerical method. Finally, some numerical results show the diffusion behaviour according to the order of space-fractional derivative and demonstrate that our ? is computationally simple for ?.