Computer algebra resolves a multitude of microscale interactions to model stochastic partial differential equations

Abstract

[Abstract]: The computer algebra routines documented here empower you to reproduce and check many of the details described by Roberts (2006). We consider a small spatial domain, representing a finite element, and apply stochastic centre manifold techniques to derive a one degree of freedom model for the dynamics in the element. The approach automatically parametrises the microscale structures induced by spatially varying stochastic noise within the element. The crucial aspect of this work is that we explore how many noise processes may interact in nonlinear dynamics.