## Illinois Journal of Mathematics

### On numerical solutions of the stochastic wave equation

John B. Walsh

#### 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.

#### Article information

Source
Illinois J. Math., Volume 50, Number 1-4 (2006), 991-1018.

Dates
First available in Project Euclid: 12 November 2009

https://projecteuclid.org/euclid.ijm/1258059497

Digital Object Identifier
doi:10.1215/ijm/1258059497

Mathematical Reviews number (MathSciNet)
MR2247851

Zentralblatt MATH identifier
1108.60058

#### Citation

Walsh, John B. On numerical solutions of the stochastic wave equation. Illinois J. Math. 50 (2006), no. 1-4, 991--1018. doi:10.1215/ijm/1258059497. https://projecteuclid.org/euclid.ijm/1258059497