Sharp convergence rates of time discretization for stochastic time-fractional PDEs subject to additive space-time white noise

Max Gunzburger, Buyang Li, Jilu Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

12 Citations (Scopus)

Abstract

The stochastic time-fractional equation ∂ t Ψ - Δ∂ t 1-α Ψ = f + W˙ with space-time white noise W˙ is discretized in time by a backward-Euler convolution quadrature for which the sharp-order error estimate (E||Ψ(·, t n ) - Ψ n || L 2 (O) 2 )) 1/2 = O(τ 1/2 - αd/4 ) is established for α ∈ (0, 2/d), where d denotes the spatial dimension, Ψ n the approximate solution at the nth time step, and E the expectation operator. In particular, the result indicates sharp convergence rates of numerical solutions for both stochastic subdiffusion and diffusion-wave problems in one spatial dimension. Numerical examples are presented to illustrate the theoretical analysis.

Original languageEnglish
Pages (from-to)1715-1741
Number of pages27
JournalMathematics of Computation
Volume88
Issue number318
DOIs
Publication statusPublished - 27 Nov 2018

Keywords

  • Error estimates
  • Space-time white noise
  • Stochastic partial differential equation
  • Time-fractional derivative

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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