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Modified DTS Iteration Methods for Spatial Fractional Diffusion Equations

Author

Listed:
  • Xin-Hui Shao

    (College of Sciences, Northeastern University, Shenyang 110819, China)

  • Chong-Bo Kang

    (College of Sciences, Northeastern University, Shenyang 110819, China)

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.

Suggested Citation

  • Xin-Hui Shao & Chong-Bo Kang, 2023. "Modified DTS Iteration Methods for Spatial Fractional Diffusion Equations," Mathematics, MDPI, vol. 11(4), pages 1-10, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:931-:d:1066035
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    References listed on IDEAS

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    1. Meerschaert, Mark M. & Scalas, Enrico, 2006. "Coupled continuous time random walks in finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 114-118.
    2. Kundu, Snehasis, 2018. "Suspension concentration distribution in turbulent flows: An analytical study using fractional advection–diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 135-155.
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