Accelerated Spatial Approximations for Time Discretized Stochastic Partial Differential Equations

Eric Joseph Hall (Lead / Corresponding author)

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

The present article investigates the convergence of a class of space-time discretization schemes for the Cauchy problem for linear parabolic stochastic partial differential equations defined on the whole space. Sufficient conditions are given for accelerating the convergence of the scheme with respect to the spatial approximation to higher order accuracy by an application of Richardson's method. This work extends the results of Gyöngy and Krylov [SIAM J. Math. Anal., 42 (2010), pp. 2275--2296] to schemes that discretize in time as well as space.
Original languageEnglish
Pages (from-to)3162-3185
Number of pages24
JournalSIAM Journal on Mathematical Analysis
Volume44
Issue number4
Early online date11 Sep 2012
DOIs
Publication statusPublished - 11 Sep 2012

Keywords

  • SPDE
  • Parabolic
  • Finite difference methods
  • Richardson's method
  • Extrapolation
  • Numerical analysis
  • Stochastic processes
  • A priori error analysis

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