On numerical solutions of the stochastic wave equation
Walsh, John B.
Illinois J. Math., Tome 50 (2006) no. 1-4, p. 991-1018 / Harvested from Project Euclid
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We show that there is a numerical scheme for the stochastic wave equation which converges in $L^p$ at a rate of $O(\sqrt h)$, and which converges a.s. uniformly on compact sets at a rate $O(\sqrt{ h|\log h|^\ep})$\,, for any $\ep >0$\,, where $h$ is the step size in both time and space. We show that this is the optimal rate: there is no scheme depending on the same increments of white noise which has a higher order of convergence.
Publié le : 2006-05-15
Classification:  60H35,  60H15,  65C30,  65M70 
@article{1258059497,
     author = {Walsh, John B.},
     title = {On numerical solutions of the stochastic wave equation},
     journal = {Illinois J. Math.},
     volume = {50},
     number = {1-4},
     year = {2006},
     pages = { 991-1018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258059497}
}

Walsh, John B. On numerical solutions of the stochastic wave equation. Illinois J. Math., Tome 50 (2006) no. 1-4, pp.  991-1018. http://gdmltest.u-ga.fr/item/1258059497/