Modified DTS Iteration Methods for Spatial Fractional Diffusion Equations

Xin-Hui Shao () and Chong-Bo Kang
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Xin-Hui Shao: College of Sciences, Northeastern University, Shenyang 110819, China
Chong-Bo Kang: College of Sciences, Northeastern University, Shenyang 110819, China

Mathematics, 2023, vol. 11, issue 4, 1-10

Abstract: For the discretized linear systems of the spatial fractional diffusion equations, we construct a class of a modified DTS iteration method and give its asymptotic convergence conditions. Then, we design a fast modified DTS preconditioner by replacing Toeplitz matrix T with the τ matrix to accelerate the convergence rates of GMRES method. Theoretically, we show that the spectrum of fast modified DTS preconditioned matrix is clustered around one. Numerical experiments verify the validity of the constructed fast modified DTS preconditioner for GMRES method.

Keywords: spatial fractional diffusion equations; convergence; preconditioner; GMRES (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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