61 citations · 202 across the 47 of their papers we have counts for
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Resolution of subgrid microscale interactions enhances the discretisation of nonautonomous partial differential equations
J. E. Bunder, A. J. Roberts
Coarse grained, macroscale, spatial discretisations of nonlinear nonautonomous partial differential\difference equations are given novel support by centre manifold theory. Dividing…
Center manifolds for infinite dimensional random dynamical systems
Xiaopeng Chen, Anthony J. Roberts, Jinqiao Duan
Stochastic center manifolds theory are crucial in modelling the dynamical behavior of complex systems under stochastic influences. A multiplicative ergodic theorem on Hilbert space…
Macroscale, slowly varying, models emerge from the microscale dynamics in long thin domains
A. J. Roberts
Many practical approximations in physics and engineering invoke a relatively long physical domain with a relatively thin cross-section. In this scenario we typically expect the sys…
Numerical integration of ordinary differential equations with rapidly oscillatory factors
J. E. Bunder, A. J. Roberts
We present a methodology for numerically integrating ordinary differential equations containing rapidly oscillatory terms. This challenge is distinct from that for differential equ…