Projects per year
Personal profile
Research interests
Numerical time-stepping methods which preserve geometric properties of time-symmetric and Hamiltonian problems over very long times. In particular, the analysis and construction of general linear methods (GLMs), which are a generalization of Runge-Kutta and linear multistep methods.
Recent work with Prof John Butcher (University of Auckland) and Terence Norton (PhD student, Bath) has shown that G-symplectic time-symmetric GLMs can solve non-separable Hamiltonian systems more efficiently than symplectic Runge- Kutta methods. Methods up to order 6 have been constructed. The underlying one-step method of such methods has been shown to be both symmetric and symplectic.
A study of starting and finishing methods has led to a re-evaluation of the way that classical numerical methods, such as Leapfrog and Crank-Nicolson, should be implemented on symplectic and near symplectic systems, such as the equations modelling weather.
Other interests include nonautonomous stability for both continuous and discrete dynamical systems.
Fingerprint Dive into the research topics where Adrian Hill is active. These topic labels come from the works of this person. Together they form a unique fingerprint.
- 3 Similar Profiles
General Linear Methods
Mathematics
Differential equations
Engineering & Materials Science
Linear multistep Methods
Mathematics
Hamiltonians
Engineering & Materials Science
Symplectic Methods
Mathematics
Generalized Eigenproblem
Mathematics
Linear Time-varying Systems
Mathematics
Algebraic Riccati Equation
Mathematics
Network
Recent external collaboration on country level. Dive into details by clicking on the dots.
Projects 2009 2012
- 2 Finished
General Linear Methods for Symplectic and Time-Reversible Problems
29/03/09 → 29/04/09
Project: Research council
Research Output 2002 2019
- 16 Article
Error estimates for semi-Lagrangian finite difference methods applied to Burgers' equation in one dimension
Cook, S., Budd, C., Hill, A. & Melvin, T., 21 Jun 2019, In : Applied Numerical Mathematics. 145, p. 261-282 22 p.Research output: Contribution to journal › Article
5
Citations
(Scopus)
79
Downloads
(Pure)
Symmetric general linear methods
Butcher, J. C., Hill, A. T. & Norton, T. J. T., 1 Dec 2016, In : BIT Numerical Mathematics. 56, 4, p. 1189-1212 24 p.Research output: Contribution to journal › Article
Open Access
File
General Linear Methods
Runge Kutta methods
Differential equations
Symmetry
One-step Method
An iterative starting method to control parasitism for the Leapfrog method
Hill, A. & Norton, T., 1 Jan 2015, In : Applied Numerical Mathematics. 87, 1, p. 145 156 p., Volume 87.Research output: Contribution to journal › Article
File
Hamiltonians
Iteration
Computational Results
Euler equations
Time Scales
14
Citations
(Scopus)
63
Downloads
(Pure)
The control of parasitism in $G$-symplectic methods
Butcher, J. C., Habib, Y., Hill, A. T. & Norton, T. J. T., 14 Oct 2014, In : SIAM Journal on Numerical Analysis (SINUM). 52, 5, p. 2440-2465 26 p.Research output: Contribution to journal › Article
Open Access
File
Symplectic Methods
Hamiltonians
General Linear Methods
Cancel
Small Perturbations
10
Citations
(Scopus)
Exponential stability of time-varying linear systems
Hill, A. T. & Ilchmann, A., Jul 2011, In : IMA Journal of Numerical Analysis. 31, 3, p. 865-885 21 p.Research output: Contribution to journal › Article
Linear Time-varying Systems
Exponential Stability
Asymptotic stability
Linear systems
Stability Estimates
Thesis
Structure-preserving General Linear Methods
Author: Norton, T., 29 Sep 2015Supervisor: Hill, A. (Supervisor)
Student thesis: Doctoral Thesis › PhD
File