A generalization of trigonometric transform splitting methods for spatial fractional diffusion equations. (15th March 2020) - Shao, Xin-Hui; Zhang, Zhen-Duo; Shen, Hai-Long
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.