摘要
通过对空间分数阶导数采用修正的Grunwald有限差分逼近,给出了数值求解时间-空间分数阶导数对流扩散方程的一种隐式差分格式.证明了格式的兼容性、无条件稳定性及一阶收敛性,并给出了数值算例.
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. First-order consistency, unconditional stability, and （therefore） first-order convergence of the method are proved using a novel shifted version of the classical Gruenwald 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.
出处
《南开大学学报（自然科学版）》
CAS
CSCD
北大核心
2009年第5期51-56,共6页
Acta Scientiarum Naturalium Universitatis Nankaiensis
基金
the National Natural Science Foundations of China(103016)
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
