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

David Cohen; Lluís Quer-Sardanyons

doi:10.1093/imanum/drv006

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

David Cohen, Lluís Quer-Sardanyons

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

15 Citations (Scopus)

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 language	English
Pages (from-to)	400-420
Journal	IMA Journal of Numerical Analysis
Volume	36
Issue number	1
DOIs	https://doi.org/10.1093/imanum/drv006
Publication status	Published - 1 Jan 2015

Keywords

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

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title = "A fully discrete approximation of the one-dimensional stochastic wave equation",

abstract = "{\textcopyright} 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.",

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AU - Quer-Sardanyons, Lluís

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N2 - © 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.

AB - © 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.

KW - Finite differences

KW - Multiplicative noise

KW - Nonlinear stochastic wave equation

KW - stochastic trigonometric methods

KW - Strong convergence

U2 - 10.1093/imanum/drv006

DO - 10.1093/imanum/drv006

M3 - Article

VL - 36

SP - 400

EP - 420

JO - IMA Journal of Numerical Analysis

JF - IMA Journal of Numerical Analysis

SN - 0272-4979

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ER -