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

Zhi Zhao, Xiao Qing Jin, Matthew M. Lin

研究成果: Article同行評審

18 引文 斯高帕斯(Scopus)

摘要

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.

原文English
頁(從 - 到)266-279
頁數14
期刊Journal of Computational Physics
319
DOIs
出版狀態Published - 2016 八月 15

All Science Journal Classification (ASJC) codes

  • 數值分析
  • 建模與模擬
  • 物理與天文學(雜項)
  • 物理與天文學 (全部)
  • 電腦科學應用
  • 計算數學
  • 應用數學

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