The Accurate Dynamic Modelling of Contaminant Dispersion in Channels. - Simon D. Watt; Anthony J. Roberts (SIAM J. Appl. Math., 1995)

Computational Models for Materials with Shape Memory: Towards a Systematic Description of Coupled Phenomena. - Roderick V. N. Melnik; Anthony J. Roberts (International Conference on Computational Science (2), 2002)

A holistic finite difference approach models linear dynamics consistently. - Anthony J. Roberts (Math. Comput., 2003)

Modelling the Dynamics of Turbulent Floods. - Anthony J. Roberts; Z. Mei; Zhenquan Li (SIAM J. Appl. Math., 2003)

Image Processing of Finite Size Rat Retinal Ganglion Cells Using Multifractal and Local Connected Fractal Analysis. - Herbert F. Jelinek; David Cornforth; Anthony J. Roberts; Gabriel Landini; Paul David Bourke; Antony W. Iorio (Australian Conference on Artificial Intelligence, 2004)

Shear Dispersion along Circular Pipes Is Affected by Bends, but the Torsion of the Pipe Is Negligible. - Anthony J. Roberts (SIAM J. Appl. Dyn. Syst., 2004)

Resolving the Multitude of Microscale Interactions Accurately Models Stochastic Partial Differential Equations. - Anthony J. Roberts (LMS J. Comput. Math., 2006)

Accurately Model the Kuramoto-Sivashinsky Dynamics with Holistic Discretization. - T. MacKenzie; Anthony J. Roberts (SIAM J. Appl. Dyn. Syst., 2006)

General Tooth Boundary Conditions for Equation Free Modeling. - Anthony J. Roberts; Ioannis G. Kevrekidis (SIAM J. Sci. Comput., 2007)

Model Dynamics across Multiple Length and Time Scales on a Spatial Multigrid. - Anthony J. Roberts (Multiscale Model. Simul., 2009)

Simulating Stochastic Inertial Manifolds by a Backward-Forward Approach. - Xingye Kan; Jinqiao Duan; Ioannis G. Kevrekidis; Anthony J. Roberts (SIAM J. Appl. Dyn. Syst., 2013)

Self-Similarity and Attraction in Stochastic Nonlinear Reaction-Diffusion Systems. - Wei Wang; Anthony J. Roberts (SIAM J. Appl. Dyn. Syst., 2013)

Model Emergent Dynamics in Complex Systems. - Anthony J. Roberts (SIAM, 2015)

Numerical integration of ordinary differential equations with rapidly oscillatory factors. - J. E. Bunder; Anthony J. Roberts (J. Comput. Appl. Math., 2015)

Splitting in systems of PDEs for two-phase multicomponent flow in porous media. - S. Borazjani; Anthony J. Roberts; Pavel G. Bedrikovetsky (Appl. Math. Lett., 2016)

Accuracy of Patch Dynamics with Mesoscale Temporal Coupling for Efficient Massively Parallel Simulations. - J. E. Bunder; Anthony J. Roberts; Ioannis G. Kevrekidis (SIAM J. Sci. Comput., 2016)

Resolution of subgrid microscale interactions enhances the discretisation of nonautonomous partial differential equations. - J. E. Bunder; Anthony J. Roberts (Appl. Math. Comput., 2017)

Good coupling for the multiscale patch scheme on systems with microscale heterogeneity. - J. E. Bunder; Anthony J. Roberts; Ioannis G. Kevrekidis (J. Comput. Phys., 2017)

Large-scale simulation of shallow water waves with computation only on small staggered patches. - J. E. Bunder; J. Divahar; Ioannis G. Kevrekidis; Trent W. Mattner; Anthony J. Roberts (CoRR, 2019)

Rigorous modelling of nonlocal interactions determines a macroscale advection-diffusion PDE. - Anthony J. Roberts (CoRR, 2020)

A multiscale scheme accurately simulates macroscale shocks in an equation-free framework. - John Maclean; J. E. Bunder; Anthony J. Roberts (CoRR, 2020)

Linking Machine Learning with Multiscale Numerics: Data-Driven Discovery of Homogenized Equations. - Hassan Arbabi; Judith E. Bunder; Giovanni Samaey; Anthony J. Roberts; Ioannis G. Kevrekidis (CoRR, 2020)

A toolbox of equation-free functions in Matlab/Octave for efficient system level simulation. - John Maclean; Judith E. Bunder; Anthony J. Roberts (Numer. Algorithms, 2021)

Equation-free patch scheme for efficient computational homogenisation via self-adjoint coupling. - J. E. Bunder; Ioannis G. Kevrekidis; Anthony J. Roberts (Numerische Mathematik, 2021)

Staggered grids for multidimensional multiscale modelling. - J. Divahar; Anthony J. Roberts; Trent W. Mattner; Judith E. Bunder; Ioannis G. Kevrekidis (CoRR, 2022)

Two novel families of multiscale staggered patch schemes efficiently simulate large-scale, weakly damped, linear waves. - J. Divahar; Anthony J. Roberts; Trent W. Mattner; Judith E. Bunder; Ioannis G. Kevrekidis (CoRR, 2022)

Adaptively Detect and Accurately Resolve Macro-scale Shocks in an Efficient Equation-Free Multiscale Simulation. - John Maclean; J. E. Bunder; Ioannis G. Kevrekidis; Anthony J. Roberts (SIAM J. Sci. Comput., 2022)

Accurate and efficient multiscale simulation of a heterogeneous elastic beam via computation on small sparse patches. - Anthony J. Roberts; Thien Tran-Duc; Judith E. Bunder; Yannis G. Kevrekidis (CoRR, 2023)

Efficient computational homogenisation of 2D beams of heterogeneous elasticity using the patch scheme. - Thien Tran-Duc; J. E. Bunder; Anthony J. Roberts (CoRR, 2023)