A GPIU method for fractional diffusion equations

Advances in Difference Equations

Hai-Long Shen¹  Yu-Han Li¹  Xin-Hui Shao¹ 

[1] Department of Mathematics, College of Sciences, Northeastern University;

关键词: Fractional diffusion equations;    Generalized saddle point problem;    Stability;    Toeplitz linear system;    The shifted Grünwald formula;   

DOI  :  10.1186/s13662-020-02731-9

来源: DOAJ

【 摘 要 】

Abstract The fractional diffusion equations can be discretized by applying the implicit finite difference scheme and the unconditionally stable shifted Grünwald formula. Hence, the generating linear system has a real Toeplitz structure when the two diffusion coefficients are non-negative constants. Through a similarity transformation, the Toeplitz linear system can be converted to a generalized saddle point problem. We use the generalization of a parameterized inexact Uzawa (GPIU) method to solve such a kind of saddle point problem and give a new algorithm based on the GPIU method. Numerical results show the effectiveness and accuracy for the new algorithm.

【 授权许可】

Unknown