Analysis of a splitting method for stochastic balance laws

Abstract

We analyse a semidiscrete splitting method for conservation laws driven by a semilinear noise term. Making use of fractional bounded variation (BV) estimates, we show that the splitting method generates approximate solutions converging to the exact solution, as the time step Δt→0 . Under the assumption of a homogenous noise function, and thus the availability of BV estimates, we provide an L1 -error estimate. Bringing into play a generalization of Kružkov’s entropy condition, permitting the ‘Kružkov constants’ to be Malliavin differentiable random variables, we establish an L1 -convergence rate of order 13 in Δt . The final version of this research has been published in IMA Journal of Numerical Analysis. © 2017 Oxford University Press