A fully discrete approximation of the one-dimensional stochastic wave equation

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Abstract

© 2015 The Authors. A fully discrete approximation of one-dimensional nonlinear stochastic wave equations driven by multiplicative noise is presented. A standard finite difference approximation is used in space and a stochastic trigonometric method is used for the temporal approximation. This explicit time integrator allows for error bounds in Lp(Ω), uniformly in time and space, in such a way that the time discretization does not suffer from any kind of CFL-type step-size restriction. Moreover, uniform almost sure convergence of the numerical solution is also proved. Numerical experiments are presented and confirm the theoretical results.
Original languageEnglish
Pages (from-to)400-420
JournalIMA Journal of Numerical Analysis
Volume36
Issue number1
DOIs
Publication statusPublished - 11 Jul 2014

Keywords

  • Finite differences
  • Multiplicative noise
  • Nonlinear stochastic wave equation
  • stochastic trigonometric methods
  • Strong convergence

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