Computer algebra derives discretisations of the stochastically forced Burgers' partial differential equation

Abstract

[Abstract]: The computer algebra routine documented here empowers you to reproduce and check many of the details described elsewhere. We consider a region of a spatial domain far from any boundaries, and apply stochastic centre manifold techniques to derive a discrete model for the dynamics. The approach automatically parametrises the microscale structures induced by spatially varying stochastic noise within each element. The crucial aspect of this work is that we explore how many noise processes and neighbouring elements may interact in nonlinear dynamics.