103 citations · 219 across the 14 of their papers we have counts for
14 papers
Normal form transforms separate slow and fast modes in stochastic dynamical systems
A. J. Roberts
Modelling stochastic systems has many important applications. Normal form coordinate transforms are a powerful way to untangle interesting long term macroscale dynamics from detail…
Resolve subgrid microscale interactions to discretise stochastic partial differential equations
A. J. Roberts
Constructing discrete models of stochastic partial differential equations is very delicate. Stochastic centre manifold theory provides novel support for coarse grained, macroscale,…
A corrected quadrature formula and applications
Nenad Ujevic, A. J. Roberts
A straightforward 3-point quadrature formula of closed type is derived that improves on Simpson's rule. Just using the additional information of the integrand's derivative at the t…
Holistically discretise the Swift-Hohenberg equation on a scale larger than its spatial pattern
A. J. Roberts
I introduce an innovative methodology for deriving numerical models of systems of partial differential equations which exhibit the evolution of spatial patterns. The new approach d…
Derive boundary conditions for holistic discretisations of Burgers' equation
A. J. Roberts
I previously used Burgers' equation to introduce a new method of numerical discretisation of \pde{}s. The analysis is based upon centre manifold theory so we are assured that the d…
An Accurate Lubrication Model of Contaminated Coating Flows
A. J. Roberts, M. E. Simpson
The levelling of short-wave irregularities on a thin film of fluid is primarily due to the action of surface tension. Surface tension gradients are often created by a number of dif…