摘要
本文考虑一个空间-时间分数阶对流扩散方程.这个方程是将一般的对流扩散方程中的时间一阶导数用α(0<α<1)阶导数代替,空间二阶导数用β(1<β<2)阶导数代替.本文提出了一个隐式差分格式,验证了这个格式是无条件稳定的,并证明了它的收敛性,其收敛阶为O(τ+h).最后给出了数值例子.
In this paper, a space-time fractional convection-diffusion equation is considered. The equation is obtained from the classical convection-diffusion equation by replacing the first- order time derivative, the second-order space derivative with fractional derivatives of order α（0 〈 α 〈 1）, β （1 〈 β 〈 2）respectively. An implicit difference scheme is presented. It is shown that the method is unconditional stable and the convergence order of the method is O（τ ＋ h） . Finally, some numerical examples are given.
出处
《计算数学》
CSCD
北大核心
2008年第3期305-310,共6页
Mathematica Numerica Sinica
关键词
对流扩散方程
分数阶导数
隐式差分格式
稳定性
收敛性
convection-diffusion equation
fractional-order derivative, implicit difference scheme
stability
convergence
