Preconditioned iterative methods for space-time fractional advection-diffusion equations

Zhi Zhao, Xiao Qing Jin, Matthew M. Lin

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

In this paper, we propose practical numerical methods for solving a class of initial-boundary value problems of space-time fractional advection-diffusion equations. First, we propose an implicit method based on two-sided Grünwald formulae and discuss its stability and consistency. Then, we develop the preconditioned generalized minimal residual (preconditioned GMRES) method and preconditioned conjugate gradient normal residual (preconditioned CGNR) method with easily constructed preconditioners. Importantly, because resulting systems are Toeplitz-like, fast Fourier transform can be applied to significantly reduce the computational cost. We perform numerical experiments to demonstrate the efficiency of our preconditioners, even in cases with variable coefficients.

Original languageEnglish
Pages (from-to)266-279
Number of pages14
JournalJournal of Computational Physics
Volume319
DOIs
Publication statusPublished - 2016 Aug 15

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All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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