Journal of Applied Mathematics and Computing

, Volume 22, Issue 3, pp 87–99

# Implicit difference approximation for the time fractional diffusion equation

• P. Zhuang
• F. Liu
Article

## Abstract

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order 0 < α < 1 ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent withO(Τ +h 2), where Τ andh are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

## AMS Mathematics Subject Classification

65L20 34D15 34K26

## Key words and phrases

Fractional differential equation implicit difference approximation stability convergence

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