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

• 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)" style="position: relative;" tabindex="0" id="MathJax-Element-1-Frame" class="MathJax">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.

Subject headings

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

nonlinear stochastic wave equation

multiplicative noise

strong convergence

finite differences

ochastic trigonometric methods

Publication and Content Type

ref (subject category)

art (subject category)