摘要
In this paper,we consider a Riesz space-fractional reaction-dispersion equation (RSFRDE).The RSFRDE is obtained from the classical reaction-dispersion equation by replacing the second-order space derivative with a Riesz derivative of orderβ∈(1,2]. We propose an implicit finite difference approximation for RSFRDE.The stability and convergence of the finite difference approximations are analyzed.Numerical results are found in good agreement with the theoretical analysis.
In this paper, we consider a Riesz space-fractional reaction-dispersion equation （RSFRDE）. The RSFRDE is obtained from the classical reaction-dispersion equation by replacing the second-order space derivative with a Riesz derivative of order β∈ （1, 2]. We propose an implicit finite difference approximation for RSFRDE. The stability and convergence of the finite difference approximations are analyzed. Numerical results are found in good agreement with the theoretical analysis.
基金
The authors gratefully acknowledge the support of the National Natural Science Foundation of China under Grant 10271098
the Australian Research Council grant LP0348653.
关键词
分数次导数
分形反应-色散方程
隐式有限差分近似
稳定性
收敛性
Riesz fractional derivative
fractional reaction-dispersion equation
implicit finite difference approximation
stability
convergence.
