Correction of high-order BDF convolution adrature for fractional evolution equations

Bangti Jin, Buyang Li, Zhi Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

71 Citations (Scopus)

Abstract

We develop proper correction formulas at the starting k − 1 steps to restore the desired kth-order convergence rate of the k-step BDF convolution quadrature for discretizing evolution equations involving a fractional-order derivative in time. The desired kth-order convergence rate can be achieved even if the source term is not compatible with the initial data, which is allowed to be nonsmooth. We provide complete error estimates for the subdiffusion case α ∈ (0, 1) and sketch the proof for the diffusion-wave case α ∈ (1, 2). Extensive numerical examples are provided to illustrate the effectiveness of the proposed scheme.
Original languageEnglish
Pages (from-to)A3129-A3152
JournalSIAM Journal on Scientific Computing
Volume39
Issue number6
DOIs
Publication statusPublished - 1 Jan 2017

Keywords

  • Backward differentiation formulas
  • Convolution quadrature
  • Error estimates
  • Fractional evolution equation
  • Incompatible data
  • Initial correction
  • Nonsmooth

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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