Abstract
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.
Citation
John B. Walsh. "On numerical solutions of the stochastic wave equation." Illinois J. Math. 50 (1-4) 991 - 1018, 2006. https://doi.org/10.1215/ijm/1258059497
Information