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A generalization of trigonometric transform splitting methods for spatial fractional diffusion equations. (English) Zbl 1443.65140
Summary: 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.
MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
Software:
FODE; ma2dfc
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