4 citations · 6 across the 2 of their papers we have counts for
5 papers
Accurate macroscale modelling of spatial dynamics in multiple dimensions
A. J. Roberts, Tony MacKenzie, J. E. Bunder
Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular…
Computer algebra derives the slow manifold of patch or element dynamics on lattices in two dimensions
Tony MacKenzie, A. J. Roberts
Developments in dynamical systems theory provides new support for the discretisation of \pde{}s and other microscale systems. Here we explore the methodology applied to the gap-too…
Holistic discretisation ensures fidelity to dynamics in two spatial dimensions
Tony MacKenzie, A. J. Roberts
Developments in dynamical systems theory provides new support for the discretisation of \pde{}s and other microscale systems. By systematically resolving subgrid microscale dynamic…
Accurately model the Kuramoto--Sivashinsky dynamics with holistic discretisation
T. MacKenzie, A. J. Roberts
We analyse the nonlinear Kuramoto--Sivashinsky equation to develop accurate discretisations modeling its dynamics on coarse grids. The analysis is based upon centre manifold theory…
Holistic finite differences accurately model the dynamics of the Kuramoto-Sivashinsky equation
T. MacKenzie, A. J. Roberts
We analyse the nonlinear Kuramoto-Sivashinsky equation to develop an accurate finite difference approximation to its dynamics. The analysis is based upon centre manifold theory so…