Accessible Requires Authentication Published by De Gruyter January 25, 2010

Finite difference approximations for space–time fractional partial differential equation

Y. Zhang
From the journal

Abstract

An implicit difference scheme is presented for a space–time fractional convection–diffusion equation. The equation is obtained from the classical integer order convection–diffusion equations with fractional order derivatives for both space and time. First-order consistency, unconditional stability, and first-order convergence of the method are proven using a novel shifted version of the classical Grünwald finite difference approximation for the fractional derivatives. A numerical example with known exact solution is also presented, and the behavior of the error is examined to verify the order of convergence.

Received: 2007-05-30
Revised: 2009-05-01
Published Online: 2010-01-25
Published in Print: 2009-December

© de Gruyter 2009