A generalization of trigonometric transform splitting methods for spatial fractional diffusion equations. (15th March 2020)

• Record Type: Journal Article
• Authors: Shao, Xin-Hui; Zhang, Zhen-Duo; Shen, Hai-Long
• Is Part Of: Computers & mathematics with applications. Volume 79:issue 6(2020)
• Page Start: 1845
• Page End: 1856
• Publication Date: 2020-03-15
• Subjects: Spatial fractional diffusion equation -- Toeplitz linear system -- Two parameters -- Trigonometric transformation splitting; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2019.10.003
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: The spatial fractional diffusion equation can be discretized by employing the implicit finite difference scheme with the shifted Grünwald formula and the given discretized linear systems have a diagonal-plus-Toeplitz structure. In this paper, based on trigonometric transformation splitting (TTS), we study efficient iterative method called GTTS has two parameters. As a focus, we give the simple and effective optimal forms of these two parameters respectively. We carry out some numerical experiments to illustrate the effectiveness and accuracy of this new algorithm.