Stability and Convergence of an Implicit Difference Approximation for the Space Riesz Fractional Reaction-Dispersion Equation  

作　　者：Jinghua Chen Fawang Liu 

机构地区：[1]College of Mathematics, Jimei University, Xiamen 361021, China [2]School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia

出　　处：《Numerical Mathematics A Journal of Chinese Universities(English Series)》2007年第3期253-264,共12页

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.

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.

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 

分 类 号：O175.2[理学—数学]