TY - JOUR
T1 - A fully discrete approximation of the one-dimensional stochastic wave equation
AU - Cohen, David
AU - Quer-Sardanyons, Lluís
PY - 2015/1/1
Y1 - 2015/1/1
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
UR - https://www.scopus.com/pages/publications/84959863127
U2 - 10.1093/imanum/drv006
DO - 10.1093/imanum/drv006
M3 - Article
SN - 0272-4979
VL - 36
SP - 400
EP - 420
JO - IMA Journal of Numerical Analysis
JF - IMA Journal of Numerical Analysis
IS - 1
ER -