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Full discretisation of semi-linear stochastic wave equations driven by multiplicative noise

Rikard Anton ; David Cohen ; Stig Larsson (Institutionen för matematiska vetenskaper, matematik) ; Xiaojie Wang
(2015)
[Preprint]

A fully discrete approximation of the semi-linear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in space and a stochastic trigonometric method for the temporal approximation. This explicit time integrator allows for mean-square error bounds indepen- dent of the space discretisation and thus do not suffer from a step size restriction as in the often used Störmer-Verlet- leap-frog scheme. Furthermore, it satisfies an almost trace formula (i. e., a linear drift of the expected value of the energy of the problem). Numerical experiments are presented and confirm the theoretical results.

Nyckelord: Semi-linear stochastic wave equation, Multiplicative noise, Strong convergence, Trace formula, Stochastic trigonometric methods, Geometric numerical integration



Denna post skapades 2015-03-13. Senast ändrad 2015-03-13.
CPL Pubid: 213766

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Numerisk analys

Chalmers infrastruktur