25 citations · 68 across the 14 of their papers we have counts for
14 papers
Normal forms and invariant manifolds for nonlinear, non-autonomous PDEs, viewed as ODEs in infinite dimensions
Peter Hochs, A. J. Roberts
We prove that a general class of nonlinear, non-autonomous ODEs in Fréchet spaces are close to ODEs in a specific normal form, where closeness means that solutions of the normal fo…
Backwards theory supports modelling via invariant manifolds for non-autonomous dynamical systems
A. J. Roberts
This article establishes the foundation for a new theory of invariant/integral manifolds for non-autonomous dynamical systems. Current rigorous support for dimensional reduction mo…
Smooth subgrid fields underpin rigorous closure in spatial discretisation of reaction-advection-diffusion PDEs
G. A. Jarrad, A. J. Roberts
Finite difference/element/volume methods of discretising PDEs impose a subgrid scale interpolation on the dynamics. In contrast, the holistic discretisation approach developed here…
Modelling suspended sediment in environmental turbulent fluids
Meng Cao, A. J. Roberts
Modelling sediment transport in environmental turbulent fluids is a challenge. This article develops a sound model of the lateral transport of suspended sediment in environmental f…
Multiscale modelling couples patches of nonlinear wave-like simulations
Meng Cao, A. J. Roberts
The multiscale gap-tooth scheme is built from given microscale simulations of complicated physical processes to empower macroscale simulations. By coupling small patches of simulat…
Modify the Improved Euler scheme to integrate stochastic differential equations
A. J. Roberts
A practical and new Runge--Kutta numerical scheme for stochastic differential equations is explored. Numerical examples demonstrate the strong convergence of the method. The first…